OK,
Craig (I'll just do an informal response instead of an in-line response - hope that's alright

),
I agree that we can discern retraction, assuming we have accurate chronological order of the texts.
What I don't think we can do is then discern the motive of why a construct was removed or added.
We cannot know this because we don't know the identity of the peoples.
We can create all sorts of logical possibilities and motives FOR them in their place.
The "Long Mark" is a great example - we could create an array of reasons someone might create this, but we can't actually employ any of those logics as proofs of truth of events until we actually know which possibility sympathizes with the peoples who valued the text (who it was for), or at least the author's culture and their culture's values of the content.
We can discern some crude aspects regarding such retractions and additions; for example, yes, we can discern that if we have our chronology correct, then the baptism appears to have altered over time.
However, can we claim that the retractions and alterations inherently indicate a hiding of Jesus' embarrassing story of being baptized for sin?
Not really; there are a host of other motives than simply embarrassment (in any means of the word).
For example:
Matthew's entry could be argued to be an expansion, not a retraction - for it is increasing the tale by adding a motive (an explanation of why Jesus was being baptized) which was not explicit in Mark.
Why? Well; that depends on who we identify this as.
If we are going to identify this as Metropolitan Egyptian Jews as the culture of interest, then it would be of value to clear up the explicit motive for this specific washing and one would need to show humility as to not offend the status of
either John or Jesus to the Egyptian Jewish mindset; for it would be equally offensive
to John to not refuse Jesus' baptism in such a culture.
But that is IF such a demographic were so accurately appointed as the intended cultural body of reception or authorship of the text.
Luke does not have anything like this explanation and is akin to Mark's version, but instead adds the context that John was baptizing other people.
Could this be out of embarrassment?
Possible; or it could be that they didn't employ Matthew's Hebrew-centric narrative (or perhaps didn't have Matthew at all) and in referring to the clearly Markan version of the tale, felt that it was needed to inform their reading audience what it was that John does normally by placing John in his normal setting (scene) when Jesus arrives.
Perhaps they aren't hiding Jesus in the crowd at all, but producing Jesus as mundane prior to the Baptism so that the subsequent scene of the heaven's opening up and the voice coming down is also more impressive and pronounced (go quiet before blaring it loud).
That is also a possibility; and one that depends on who wrote the text for whom - and we don't know.
John takes Luke's version and expands upon it further - implying that if John was baptizing people, then he must therefore be baptizing people for the purpose of the encounter with Jesus.
Why?
Is it to hide Jesus from being a simple man?
Perhaps; maybe.
But if John is the production of Anatolian theological theater (a fashion of the time), then it would have nothing to do with embarrassment and instead be about streamlining the narrative to keep the spotlight on the central character of the story and keep focus upon the primary messianic narrative.
This is also possible, but entirely rests upon - again - who wrote the text for whom...and again...we don't actually know.
Now, as to Carrier's statement about the crucifixion and the criterion of embarrassment:
This is what he actually says -
EXAMPLE 3: The Criterion of Embarrassment : “Since Christian authors would not invent
anything that would embarrass them, anything embarrassing in the tradition must be
true.”
Major Premise 1: Christians would not invent anything that would embarrass them.
Minor Premise 1: The crucifixion of Jesus would embarrass Christians.
Conclusion 1: Therefore, Christians did not invent the crucifixion of Jesus.
Major Premise 2: A report is either invented or it is true.
Minor Premise 2 (= Conclusion 1): The crucifixion of Jesus was not invented.
Conclusion 2: Therefore, the crucifixion of Jesus is true.
Another way to test rules of inference is to try them out on contrary cases. For example:
Major Premise 1: Cybeleans would not invent anything that would embarrass them.
Minor Premise 1: The castration of Attis would embarrass Cybeleans.
Conclusion 1: Therefore, Cybeleans did not invent the castration of Attis.
Major Premise 2: A report is either invented or it is true.
Minor Premise 2 (= Conclusion 1): The castration of Attis was not invented.
Conclusion 2: Therefore, the castration of Attis is true.
RESULT: This is obviously not a credible conclusion. We have no good reason to believe there was ever an actual Attis who was castrated and it is commonly assumed the story was invented for some particular symbolic reason. The same, then, could be true of the crucifixion of Jesus. Tacitus reports that the castration of Attis was indeed embarrassing (it is grounds for his disgust at the religion), yet the castration of Attis is not a credible story, therefore the criterion of embarrassment is in some manner fallacious. An example within the Christian tradition is the astonishing stupidity of the Disciples, especially in the earliest Gospel of Mark. Their depiction is in fact so unrealistic it isn’t credible (real people don’t act like that), which means Mark (or his sources) invented that detail despite its potential embarrassment. Hence the flaw in the criterion of embarrassment is in assuming that historical truth is the only factor that can overcome the potential embarrassment of some reported detail, when in fact moral or doctrinal or symbolic truth can also override such concerns. For example, Dennis MacDonald argues this attribute emulates the equally unrealistic stupidity of the crew of Odysseus and thus stands as a marker of the same things that their stupidity represented. That may be true. But I also argue it furthers a literary theme found throughout Mark of the Reversal of Expectation. Thus everything that seems embarrassing in Mark might be an intentional fabrication meant to convey a lesson. Mark echoes the gospel theme that “the least shall be first” in his construction of all his stories: although Jesus tells Simon Peter he must take up the cross and follow him, Simon the Cyrenean does this instead; although the pillars James and John debate who will sit at Jesus’ right and left at the end, instead two nameless thieves sit at his right and left at the end; although the lofty male Disciples flee and abandon Jesus, the lowly female followers remain faithful, and as a result the least are the first to discover that Christ is risen; and while Mark begins his Gospel with the “good news” of the “voice crying out” of the lone man who boldly came forward as a “messenger who will prepare our way,” he ends his Gospel with several women, fleeing in fear and silence, and not delivering the
good news, exactly the opposite of how his book began. So since details that seem embarrassing in Mark might serve his literary intentions, we can’t be certain they’re true.
http://www.richardcarrier.info/CarrierDec08.pdf
It should be clear from the above that his point is about the subjective value of the concept of "embarrassment" and not about addressing some position holding that the apostles were so stupid that fact is therefore verified.
He's outlining that the possibility exists for other motives to be involved and since we cannot rule out those other possibilities; it is hasty and erroneous to draw a conclusion regarding concepts like Embarrassment as a motive.
For my thoughts on the matter:
If we take the order of the texts to be accurate, and then examine the crucifixion; another highlight of the importance of the subjective nature of the motivated value of a scene or symbol is that the crucifixion (under the classic chronology of texts) becomes more elaborate in each version - not less.
Instead of hiding or simply removing the alleged embarrassment (which would have been simple enough to do), it is being embellished and decorated with lavish trimmings beyond Mark's version.
So it could be argued flatly back that it doesn't appear to be embarrassing at all just on asking why it was left in.
If Mark was the only one that had the account and the rest were absent of it, then no one today would know the difference.
Mark would have not been accepted into Canon later; some other text in its place would have been, and the other texts without the crucifixion would have been included.
It's not like that control wasn't available and employed - it was.
So if it was in the text; it doesn't mean inherently that it was real or true - but that it had value religiously and symbolically because (if our chronology is accurate) then it appears that the event continues to grow in admiration...not in embarrassment.
But again: we cannot FULLY know until we have the cultures in our grasp explicitly.