maybe i can help you out here. I was on 8 waitlists last summer, and finally got into 3 of the schools.
LOI is the best hand you can play...play it wisely. It won't do anything for you if you're at the bottom or middle of a waitlist, but almost certainly get you in somewhere if you're on the borderline or near the top.
Even on ranked waitlists, it can make a difference. Of course, it depends on the school.
By all means send the letter of intent to your favorite, and send letters of interest to all the other schools. Make it short and simple. One paragraph on how you're still extremely interested in their program, blah blah. Attach a sheet with updated grades and activities. Don't put too much writing or they won't look at it. Send it priority or overnight, and you can be sure at least somebody in the office will pay attention to it.
Good luck. It's a stressful game, being on waitlists, but I swear there's light at the end of the tunnel...you just gotta be aggressive.