What happens when Corbyn has a tizzy and fucks off with the ball after being rejected as captain? I sincerely hope I am wrong, but 1) Corbyn is highly unlikely to agree to strict criteria about what is expected from as PM; and 2) if he is indeed rejected, he will three-line whip his PMs into not supporting any other candidate as PM. I expect no more from Corbyn than I do from Johnson. I genuinely do not know what is best in this situation.
I think your first point has some merit; Corbyn probably will expect to lead any GoNU and will not look with favour upon any suggestion that someone else does it.
He'll have clear tactical reasons for doing so - to allow himself to be overlooked as leader, while being the Leader of the Opposition, will send an almost fatal message to the world that he cannot be Prime Minister after a GE, and thus derail any GE campaign before it has started.
Can you imagine the mockery and abuse Labour would get in a post-GoNU GE campaign about their leader not even being seen as capable of leading a temporary GoNU, so how can people trust him as a potential permanent PM? In fact this goes beyond Corbyn to apply to any Labour leader, even of Corbyn were to be replaced.
So in that regard Corbyn and Labour would have very good grounds for expecting to lead any GoNU.
The latter point, that he will not allow himself to be constrained by strict criteria as to what is expected of him, I don't really think is true. He will see his desired GE tantalisingly within his grasp, and with Wormtongue whispering in his ears, he will back himself to win it. So consequently I think he'd be content to take on a temporary restricted role as a constrained Leader of a temporary government, in order to actualise what he sees as his chance of becoming permanent Prime Minister.
Just the fact that he has done the role, in however restricted a form, and 'saved the nation from a disastrous NO Deal' will confer a veneer of legitimacy on him and oil the wheels, making it that little bit more likely that he might finally get over the line in a GE. At least in his eyes.
The only thing preventing the above view, IMO, is if the old accusation that he doesn't really want to be power, just perpetual opposition, turns out to be true.