; ought to have had a central message but doesn't.
He was preaching the eschaton. That he got crucified put a spanner in the works somewhat
The Qur'an was assembled as 'the sayings of Muhammad' two hundred years after his death, and western Muslim scholarship, where it's permissible to talk about such things, has no doubt that if there's any wheat in there, it's buried under a mountain of chaff. Unlike Jesus, there does appear to be at least one contemporary and independent reference fitting Mohammad, though.
I guess you mean hadith?
There are a couple of vague, incidental near-contemporary references to someone who is presumably (but not definitively) the Muhammad (1. "a prophet among the Arabs" 2. "The Arabs of Muhammad")
His biography seems to grow with the retelling and gets increasingly miraculous, but this isn't given as reason to doubt his existence. It is hagiography after all.
Let's just agree, then, that both views are possible.
Why do you believe an invented messiah would not even remotely meet the overall criteria for being the expected messiah and the few points he does meet are only through ridiculously contrived circumstances?
Why do you think Paul or whoever would invent such an implausible messiah?
Your argument ought to be stronger for a character invented between, say, 1 and 49 CE, and if there was a story, Paul, if his claims to have persecuted Christians and to have met disciples are true, ought to have had a reasonable look at it; but writing in the 50s CE he knows almost nothing of an earthly Jesus and cares even less. And the author of Mark knows little more, but sets about creating a bio, the only one we have, regardless of whether an historical Jesus had died 45 years earlier or not.
Paul was writing to communities of believers already in existence that had been formed by direct personal relationships with a small cadre of early followers, it would be a bit odd if he started by telling them who Jesus was.
You start needing a written bio more when the movement grows and you get further from events (as you see in Islam).
If you've ever looked at Graves' The Greek Myths, you'll know that nearly all of them have multiple versions, different names for the same and new characters, and so on. It's not even clear that somewhere way back there ought to have been a single first tale, instead of an evolving and fusing and dividing of tale
And all of these are tales that were around for centuries in various forms. They were not referring to near-contemporary events and figures.
Stories about Abraham, Moses, etc.and their followers didn't appear within a decade or so of their purported lives either.