My schools wanted the letters of recommendation enclosed with my application materials in one envelope. So I had my recommenders seal the letter in a business-sized envelope and sign their names across the seal. Then I just slipped the letters into the bigger envelope with my application, transcripts, etc.
7 schools is a lot of recommendation letters, esp. if there are forms that have to be filled out in addition to the letter. Make sure your recommenders are OK with doing that many *and* make sure they can be relied on to meet your deadlines. As a former college prof, I wrote many letters of recommendation, and they are work and time-eaters. Don't get me wrong; I did like writing them. But sometimes at crunch-time, it really ate away at my time to do them. So as long as your recommenders are cool with doing 7 letters, go for it.