I have heard that Columbia has long, long waitlists-- that they tend to waitlist many people and accept relatively few. NYU, on the other hand, supposedly limits their waitlist to applicants that they would actually offer a spot if one happened to open up, so your chances might be better on there.
I have heard conflicting things about the Columbia waitlist. Someone on Columbia's faculty told me that there is absolutely nothing that you can do to affect your place on the waitlist-- no recommendations etc. will help.
Most people say that that isn't true. They say that if you write a nice letter and solicit an extra LOR or two you will have better chances. There is no way to know what really goes on, as most law schools use the waitlist for "diversity" purposes-- to fill in an extra high scorer here and minority there type of thing.
I would recommend calling the schools and asking them what to do. I had already reached the max on LOR but my present employer wanted to write for me. I called a few schools that I was WL on and they told me that if you are on the WL you can go over the LOR limit.
There is def an element of luck- but every year students DO get off of these waitlists. I'm sure you know people that have. Practically everyone i know at a top law school has gotten in off waitlists, (I had friends that got off of harvard, columbia, and penn last year) so I'm trying to stay optimistic.
Best of luck!