FWIW, I am in the group that thinks that an HJ probably existed but the two arguments you put forth here are weaker than it might seem.
Well, I admit this is a minor issue academically given the sparse sources, but that's not very exceptional when it comes to ancient history studied in esoteric fragments written in esoteric languages: there can easily be only a handful of real authorities in any given subject. But I don't think this will change the basic empirical situation: there are experts on this issue and they are mostly in agreement. There are no shortcuts, not in the study of the era of Jesus, or, say, in structural mechanics of building collapses - you qualify, you publish, you get accepted, or then not. What else would be there? Internet forums?
As to the case for a composite or totally mythical figure - surely it can be made, but I don't really see where else it could be made but in the academia and within the scientific method as it is applied in historiography. How else? When I said that a historical figure behind the Jesus myth speaks to common sense and Occam, I did say "as a lay person", so to my mind I did not pretty much take any serious position on that question. (Though I have to see I have seen snake oil salesmen in the various WTC battles that have come with exactly the kind of rationalizations about Occam as Hans above...)
To sum things up: I see this as an expert issue and make, very strongly, the argument that in that case, for an amateur and lay person unable to read these manuscripts in the original, the rational way is to trust the current expert consensus. Knowing the gloria that comes when you can establish a new consensus and break genuinely new ground, it would be very difficult to believe that the applied scientific method would not ultimately work on this issue too. I don't really see the fuss at all. This is an internet forum with obviously several one issue lay crusaders - not hugely different, in kind, than the ID or WTC or NWO crowd. So which side should one, rationally, believe in your mind?