While having a pre-health committee is nice, I didnt have one. Not sure if you do or not OP, but I wouldnt send more than necessary. I would say three or four at most. Any more than that and you run a risk of having a lack luster letter in your file and casting doubt on your app even if the rest of bullet proof. It would be much better to have three or four letters of great sustinence than 7 that are kinda flaky. I would also recommend using virtual eval or interfolio, and get your letter writers to write and send them in early. That way when you hear from a school you can pop those letters out to them quickly from interfolio or whatever you decide to use.
I had a bitch of a time getting all my letters in and one of my letter writers just didnt write my letter after I had been waiting on it for almost two months. She still hasnt. Lesson? Stay on letter writers to make sure they get their stuff done. But its ok, cause I got into my number one choice thankfully without her. 🙂