It is hard to generalize, but one thing I am worried about is changing stuff if that is problematic (as it is to many who have autism). Since he just started riding the 20" in the last week, maybe let him get used to that for awhile, until it is very obviously too small (too small might mean a very different thing to him -- it might be what is giving him the confidence). Then if the frame and fork allow it, maybe 24" wheels first would be a small enough change not to induce upset.
I'd stick with what works for as long as possible.
What's a BBS?