My HS really is into math competitions too, which start in middle school mostly. Mathcounts, AMC 8/10/12, Math League, etc. AOPS has classes and short weekend jams in prep for AMC.
7th graders can look into applying for Caroline Bradley scholarship for high school. This is open to anyone with high SAT scores and achievements. Jack Cook Kent has a scholarship for 7th graders to apply for high school too - this one has an income requirement along with academic.
There are lots of potential ways to go through HS with a gifted child. Homeschooling is much easier now with online options. Stanford has a program as does Georgetown.
Good luck!