I started on the float pool too and discovered pretty fast it wasn't for me. When I saw an opening on med surg I talked to my supervisor, she was very supportive and I was able to move. I felt bad, but she said that they want the nurses to be happy and to stay. The hospital spent a lot of money training you, seems like it would be in their best interest to help you find a place that made you happy vs you taking your new training to another hospital.
Don't let a verbal contract keep you from trying. Worse they can say is no and then maybe you will need to look at switching hospitals if you want off the float team.