Without a major hook, even getting your SAT up above 1500 is still a far reach to get into Harvard, et al. I thnik you really need to be very realistic about your chances, and come up with safeties and reaches. Even for kids with spectacular grades and scores are being rejected from the elite schools, especially the Ivys. There are many other excellent schools you can apply to and get a great education without having to go to any Ivy or its equivalent.
Also if your SAT is 1200, unless you fully dedicate all your time to studying for the SAT, raising the score above 300 is extremely unlikely, especially since there isn’t much time to study before you apply.