If you will be pre-law or pre-med, I wouldn’t worry about Top 20/Ivy.
I was a patient at a top hospital - Vandy. Residents do their undergrads at places like Luther, Kansas State, Northern Illinois, and more. It’s similar at places like Duke and Johns Hopkins - yes, I’ve checked.
For law, Harvard has 146 colleges represented in its first year class. UVA’s 315 first year come from 131 schools. Last year 300 from 133 schools. Penn’s overall law school class came from more than 200 schools and a first year class of 251 from 119 schools. 73% were out of school one plus years so work experience will matter.
So - if your school limits you because of all the moving, you need to adapt and adjust and you’ll be fine.
It’s not a race - and while rigor is important, so are grades, test score (sure, take it), and more.
I also would not take math over the summer. It’s condensed and I prefer math with a live teacher. You don’t need to jump ahead and you definitely don’t need a big name college to be a doctor or lawyer from a top medical or law school.
Then there’s cost - many colleges cost a lot - and there’s Ivy level students likely at most every flagship in America.
Work within your system..if they decide you’re not ready or able for more APs, it can still work for you. Your bigger issue might be piecing all the different locations together so that it’s understood.
Best of luck.