I can’t read a theme in your EC’s. I think you would need to have more focus around what you plan to do and tie it back to what you have done. Caltech and MIT might not be the best choices. I don’t really see that in your info. UChicago seems like a better option. Having an idea regarding what you would like to study would make for a more coherent presenation. Remember these schools get the same stats over and over. Why they pick one over another is based on something that can present the candidate as a logical choice for a particular program.