I don’t think Caltech would suit you. Yes, the weather is awesome, the environment is beautiful and the exclusive one-to-one professor access (lunches and dinners at the Athenaeum) may not be available at any other university (I think). Caltech, however, is extremely tough, especially the first and second year; you may be able to do the work, but, you have to be able to work with others (ALL OF THE TIME) without being in awe of yourself.
Your plan to do everything in 3 years doesn’t suit Caltech. These students work, live and play collaboratively, yes PLAY!, a lot! For many high-achieving students, who are used to doing things alone, it doesn’t work that way at Caltech.
I don’t know you, but the micromanaging of time doesn’t allow for surprises. Caltech has surprises. Being independent and doing your own thing which, might work well at other universities, won’t work at Caltech. “Techrs” graduate together as a team. Think about your acceptances and to what you need to do.