At which top universities can I be the least well-rounded?

Most Engineering and Tech schools will have fewer general requirements than traditional liberal arts colleges will. If you have a lot of AP or IB credits, you might be able to bypass some Gen Ed requirements. You should do the ground-work yourself, however. The most elite colleges and universities base their reputations on longstanding excellence in the Arts & Sciences, and pride themselves on producing well-educated graduates. Harvard, Yale, Stanford, et al, would not enjoy their prestige if their alumnae/i could not read and write well. They can pick and choose among the most accomplished students in the world.