Regarding your SAT, if you believe you performed significantly below your potential, you should consider retaking it. A 730 math section result, for example, might provide you with a greater range of college options than your current 670.
“Brown University is one of the more extreme examples of this concept. You almost start with a blank piece of paper to design your program of studies.”
That’s not how Brown works for STEM majors, including computer science. There are a lot of requirements, it’s very prescriptive, there may be some flexibility in the humanities electives, but it is nowhere near a blank piece of paper. You have to take a lot of math classes, computer theory, etc. The BSc in CS from Brown is very similar to the CS from other colleges, which is good for Brown grads :-).