I am hearing you Marcy. We had similar concerns. We started with spending part of the day in first grade during kindergarten and using independent books not leveled reading. The teacher actually was good at math differentiation. We are not in the US but there are similar challenges everywhere.
If moving up a grade is too hard then subject acceleration is a good starting point or accelerating in place by bringing the work to him in his classroom. The difficulty we found with that is DD felt different when she worked alone and the stimulation of everyone working at a higher level adds a different dimension.
Sometimes the "immaturity" eases or goes away when the appropriate challenge level is reached but he is only a little boy too! When DD was going to first grade she used to take a teddy bear with her so she looked very young but it was fine.
Some other good books on Giftedness if you are at the early stages of the journey can include:
Giftedness 101 by Linda Silverman
A PArents Guide to Gifted Children by James Webb
And in your case
Exceptionally Gifted Children by Miraca Gross.
There are many books and resources but it can be a little overwhelming!
Websites including here, the Davidson Institute Database, Hoagies Gifted and SENG are worth bookmarking.
