Losing credibility in the eyes of the wise, though, is impossible.
Not so. Be wrong on stuff that matters when you clearly had enough evidence available to reach the correct decision (and they previously would have expected you to be correct). If that doesn't cause you to lose credibility in their eyes then I reject either your definition of "credibility" or "wise".
I guess I could just claim to be God
It would be sufficient to claim that there is a god (and it is this particular God) despite the information you had available. See above.
Thank you for your cooperation and understanding. Don't worry, there won't be future posts like this, so you don't have to delete my LessWrong account, and anyway I could make another, and another.
But since you've dared to read this far:
Credibility. Should you maximize it, or minimize it? Have I made an error?
Discuss.
Don't be shallow, don't just consider the obvious points. Consider that I've thought about this for many, many hours, and that you don't have any privileged information. Whence our disagreement, if one exists?