I actually looked at the "drive safe/ly" answers before I posted this question and remember, at the time, seeing how these were clearly two different questions. Now, however, they seem the same. I guess I didn't think I was near as drunk as I actually was.
Solved.
Near or nearly?
Between "not near as drunk" and "not nearly as drunk", I can't think of a compelling reason to prefer one to the other. "Not nearly" sounds better, I think, but I wouldn't be able to say why.
I imagine it comes down to whether "as" is an adverb or a preposition in this phrase, but I can't think of a compelling reason to decide even that one way or the other.