Ian,
Regarding the impact of a physical Jesus discovery upon Christianity.
The only way such a discovery would not negatively impact Christianity more than help it would be if the remains were absent of pathological markings of the era.
However, if the remains were any form of standard for the era - even marginally, it would be a considerable problem for the religion.
This isn't about whether or not the figure stands against some creed or not in regards to the body still existing or not; it has to do with a much larger problem - how would any divine, or even just really special healer prophet, figure be such while at the same time having medical issues in their own body?
The only versions of Christianity which would not be troubled by this are the those who only see the Jesus figure as a philosopher.
Counter to this, if no body is ever found, then that won't cause a conclusion for the religion; the religion will be free to continue to mark up Jesus however they wish as their constructs already use the absence of any body as evidence of Jesus' divinity (whether that makes logical sense to someone not in the religion or not).
Regarding Paleographic Arguments
Oh, yes; there are some texts which receive much debate (those are the fun ones

).
Regarding "Biblical Archaeology"
It is a huge problem only because of the manner in which it was done.
In fact, that period of archaeology (or said, the complete ethical failure of it) was really important as it greatly influenced the ethics of the field from that point on - it is still one of the examples of how not to do archaeology (the other staple is Egyptian archaeology of the 19th and early 20th c CE).
Regarding the Summary of a Common Argument (bulleted list)
Keep in mind that what I wrote was a very generalized summary, and that I noted that that particular argument is very poor for a forum conversation.
That particular form of argument takes far too much information being conveyed to really function in this setting.
The best that I can do here is just provide the gross outline, which each of those bullet items could be thought of like a chapter in a book.
However, in keeping in mind that while I sympathize with the argument, that I do not agree with it, I will do my best to answer some of your questions about it.
Regarding 1:
So those are not “accounts of a 'walk-among-you-daily individual' ". Those are anonymous accounts of other anonymous informants telling of legendary tales of a “walk amongst you daily miraculous messiah of God”.
That is part of the consideration; we don't even have other texts which do this in the visceral manner in which these texts do.
The caliber of daily-life constructs in the texts are impressive, regardless if we take them as complete fabrication or not.
Consider for a moment, other myths. Are we able to slide these text's tales into belonging with other myths of the cultures around in form and style?
Not directly, no.
There's clear borrowing in some manners, but nothing which clearly marks it to belonging to mythical writings of any given culture.
My considerations on these points are that it equally does not belong to biographical chronicles, as the form and style equally does not fit there.
I don't think that the previous leads to the chronicle conclusion, but instead indicates there is a new literary form and social format evolving which should not be ignored from cultural identification (something I personally feel is tragically lacking in the field).
Regarding 2:
Were there not already detailed accounts of what was done by people like Moses, Abraham, Solomon, David?
No; the absolute closest that you get is Job.
And also, I think that's something overlooked often in this argument.
That Job is the only other story which alleges such a concept as a nearly daily life type setting is, I think, not considered enough when reflecting upon the cultural formation of these texts.
However, the direct answer is no; those are not comparable stories to Jesus.
They would be if those stories were of more granular detail and revolved specifically around the individual more, but those stories are from an older period which wrote rather differently - more about the events and actions than the philosophies, they also lacked much in daily-life detail by comparison, and also focused more on being the parable instead of conveying parables within.
Regarding 3:
All the other gods from BC history who interacted with humans on earth, what about them?
Those stories are very much more like the stories of Genesis than of Jesus, and most deities of the era in this region did not interact in an personalized method - not that we can take the texts to outright be claiming that Jesus is a god, either, as that is an interpretation of theology later which constructed the divinity of Jesus using arguments derived from the texts, but not in the texts directly, or absolutely.
Regarding 4:
Yes, and those were also written scores of years following the alleged life of such individuals and events listed in them, as well, they were written by Temple Scribes and not by common hands (which these texts clearly are not written by any Temple Scribe).
Regarding 5:
Quite right; it only outlines that there is nothing of this form which denies entry into the period. That may seem small in matter, but it is important. If such didn't fit, then we probably wouldn't even be having this conversation to begin with.
Regarding the Summary of Conclusion:
Well if that’s their conclusion on the basis of the above list, then they should not be "professionals" lol. They should move to some other subject entirely.
Keep in mind that I am summarizing a large amount of information, and this is also my compressed representation of others.
They are professionals, and in the details that go into this argument in full nature, I can understand the reasoning for considering this option - it is a reasonable option.
I do not think it likely, but for reasons that have little to do with the arguments that you can find presented.
What do you mean by anthropologically speaking? Because what makes very obvious perfect sense, and what is actually a matter of proven fact, is that the messiah stories were being taken from what had been written centuries before in the OT. And the saving messiah belief was in any case the foundation of Jewish religious belief throughout that OT period and earlier from at least the time of David c.1000BC.
True, but nothing quite like this at all (also; the Jury is out on the Davidic Kingdom

- at best, the possibility of such a "Kingdom" would be quite humble indeed, based on what we have been able to find so far).
So while I say "true", I disagree with your dates.
1000 BCE is 200 years after the first archaeological distinction of Hebrew peoples separate from their fellow Canaanite family.
The texts of the "Old Testament" don't really start showing up until around (at earliest) the 9th c BCE, and mostly from about the 7th and 6th c BCE eras (
I compiled notes in a timeline [right hand side])
However, yes, messianic stories were not foreign to the Hebrew culture; what is, is the manner in which it is conveyed and the values focused upon in so doing.
If you mix Daniel and Job together and add a little Zoroaster, you kind of come close - but not exact - to these stories (which, is something that I think is particularly overlooked in the field).
Regarding the Exilic Period
The exilic period clearly occurred; that is clear as it could be.
It was not as complete as the Roman's later annihilation, and indeed Babylon set up a vassal in Judah.
However, that period clearly existed and clearly wiped out and drove out a sizable amount of the population.
Firstly, this is when the Kingdom of Israel (Northern Kingdom, counter to Kingdom of Judah in the South) was wiped from the planet to never again return.
This is also the period which marks the end of the 1st Temple Period and after which brings us the 2nd Temple Period.
Judah itself has archaeological scars from this period.
Huddlestun himself, of course rather accurately, cites the exilic period as the distinction point between pre and post-Monotheistic Hebrew culture.
So yes, this period definitely did happen, but no, the exilic period did not erase all of the peoples from the land; nor did it need to for influence of culture in literature (which, this period defines a distinction in Hebrew literature).
Regarding "Knowing"
I don’t know how we can “know” any of the above by the methods of ancient history, and certainly not if it’s just as vacuous as being “historically evident”. But if we veer off topic into discussing how we know about all those events then we will be here for at least another 1000 pages talking about things that have little or nothing to do with Jesus.
If you ever want more detail on those items, just let me know and I'd be happy to share what I am aware of regarding how we "know" these things.
Regarding the Final Thoughts
What is more certain, rather than carry on with speculation, is that since at least 500BC the OT had been centrally concerned with the belief that God would send a saving messiah. At various times that messiah was thought of in different ways, e.g. as a military or royal leader, or as a highest priestly leader etc. And by the time of the Dead Sea Scrolls it seems that the messianic belief had changed to that of a priestly apocalyptic messenger of God who/was warning the people of imminent days of final judgement. Along with that, since c.300BC the region and the people had become heavily influenced by leaders, practices and beliefs from Greece, Persia and Rome (amongst others), and particularly Greek culture and it's religious beliefs, to the extent that Jewish people in the region were no longer reading and writing in their original Hebrew language, but were actually reading and writing mostly in Greek.
What Paul was preaching as an apocalyptic religious messiah, was afaik very similar to what the DSS Essenes had been preaching around Jerusalem since at least about 170BC. So for the very little that Paul says about “Jesus” as the messiah, it’s perfectly obvious that Paul and all Jewish preachers at that time would be preaching from within a culture and environment that had already incorporated all those religious messianic influences for several centuries, i.e. influence from the Greek, Roman and Persian religions/gods, the immediately preceding and still continuing influence from the DSS Essenes (until c.70AD), and their own messiah beliefs which stretch back to the time of David c.1000BC! Not to mention that Paul and later gospel writers repeatedly make very clear that they were taking their messiah beliefs from what they thought was the true meaning of prophecy in the OT since 500BC!
Yes, textual shifts in the post-exilic period became increasingly apocalyptic and messianic; though messianic was something which really only gets a following around 1st c BCE (note: Daniel is not in the 200 BCE Hebrew Canon).
Moses is about the only "messiah"-like figure previous to the emergence of the Jesus stories - if by the term we are referring to the Messianic movement sense of the term, and not just simply the repeated use of the phrase for all prophets and praised Kings (for which, Jesus is not comparable).
Influences from other cultures stretched back much further than 300 BCE.
There really isn't an era of Hebrew culture that isn't influenced by another culture.
For Paul, DSS, and Essenes; that is far too lengthy of a conversation for here, but I have gone over it in pretty substantial detail in
Brainache's thread Paul The Herodian and the DSS.
In brief form, the DSS dates are older than 170 BCE (they correlate to the Hasmonean dynasty), there is no inherent link in full between Essenes and DSS (though there is a compelling argument for at least a partial link of some form), and there is a
dramatic difference between Pauline texts and the DSS.
In general, no, there isn't a thriving Jesus-like culture in the Hebrew culture prior to these Jesus stories.
That said; that does not compel the conclusion that Jesus therefore existed.
Instead, it just notes that a new form arose and should be noted for the influences which gave it rise (again, something that is not so widely investigated as one would expect).