Another vote for checking out Avery Coonley. I think my kid is pretty darn smart, but definitely not THAT level. Your son sounds like exactly the type of student that Avery Coonley caters to.
I DO think that District 204 will be able to accomodate your son (again, once he hits 3rd grade, and agree to supplement until then.) If you do decide to check out other private schools, there are 2 Catholic schools in the area that I suggest. The first is Saints Peter & Paul, which is right by downtown Naperville. They do have special accomodations for gifted students, and the school as a whole produces better results than Districts 203 & 204.
The other is All Saints Academy, which is just south of downtown Naperville, on Aurora. I know a family who had their kids there before they moved out of the area, and they were quite happy there. (The parents are a physcian and a genuis-level PhD.)
I know the registration deadline for both have passed, however if you contact the schools you could at least get info and see if either might have a place for them. Enrollment ends on June 1st for Ss Peter & Paul, so they might have some spots available if some families who applied at registration time do not end up enrolling.