You miss 100% of the shots you don’t take. He can always revert to the more standard programming, so why not go for it if he’s enthusiastic? A little extra difficulty could be exhilarating.
The school sounds supportive. I’d have him do both concurrently to minimize gaps and test out of the higher level class at year end, thinning out the amount of duplicate practice along the way. The worst case scenario is that he remains on track with a head start from extra exposure. He can’t lose.
Our schools are remarkably supportive compared with some horror stories I've heard! Every teacher and principal we've met, once they get to know our kids, would bend over backward for us, frankly. At this point he's dropped the Alg II, so that ship has sailed. But one idea I've tossed around to myself is getting him to do AOPS Intermediate Algebra on his own time or over the summer, and kill the "math should have problem solving" and "cover the gaps" birds with one stone. We'll see; he doesn't like math THAT much. :p
You are EXACTLY right about the exhilaration of challenge though! I also love the maturity it required for him to reach out to the teacher on the second day and ask some questions, things that weren't answered in the syllabus but maybe covered in the first weeks of class. It's hard for a gifted kid not to already know! Yay for having the opportunity to need to ask!