Well, it certainly is not a bad thing to have 7 people willing to say good things about you. I think the best option is to make sure you have people who can discuss different aspects. Each time someone can add something new/diferent to your profile (asuming they are good), it is better than having the same thing repeated (allthough confirmation is a good sgnal). Another thing to consider is the schools you are applying to, maybe someone has strong ties.
I say pick 3 that you think can speak great things about you, while maintaining a diversity i.e. a math prof, an econ prof you have done research with, and a mentor or close prof. Then for the 4th letter, just pick someone who has ties to the program you are interested in (of course only if they have good things to say).
Of course there is always the exception of people like John Nash. According to Osborne's "An Introduction to Game Theory" one of his letters of recomendation had only one sentence "This man is a genius". But since most of us are not John Nash, I think it is a good idea to have a more diversified set of recomendations that can highlight your different strengths. In the end, there will be some overlap since there are certain persoanl characteristics that every professor will see in a good student, which would bring some confirmation.
This looks to me like #1, #2, and #4 plus a fourth of your choosing (probably #5, or #6, but again, it depends where you apply) would do the trick.
I like to think that
LOR's are the most important part of an app after you make it through the cut-offs, so be selective and strategic.
Good luck