I did this essentially for the same reasons. I had a fairly good case though, as most people would agree that my old school is not very good in what I would like to do. As far as I know nobody cared to bother to contact my old school , and I also only told them after I accepted my new school*s offer. I got recommedations from the same people from whom I got in the first round. I honestly revealed my situation for these profs, so they could address it in their LORs. (actually first I asked their opinion on my situation , so they were the ones who sort of suggested me to transfer) As said before they also knew that I was not a good fit in my old school.
Transfers seem to happen quite often although I had the impression that noone would support it if they felt that you only want to do it to move to a better ranked school. Honestly you have a better chance to make a lateral move. Also I cannot transfer credits (theoretically yes practically not really). My new school sort of said that they accepted me because they can teach me what I could not study at my old institution so they expect me to study wat they have to teach.
Good luck!
