I also work for this particular hospital system. Without naming names....it used to be called one thing and now its called another. Your contract is pro rated...so you will owe less than the original amount. However just let them know you are moving, they may not hold you to the agreement. I have never understood where they come up with the 13,500 from though. Its not like they give us that. How does our training cost that much? All we do are a few sims and depending on the unit, have a preceptor for 8-15 weeks. We do way more for them than they ever do for us.
On another note..I feel the same way you do in many ways OP. I do like the people and management on my unit, but the hospital itself and the policies they push are miserable. The staffing is unsafe, we have no ancillary help and new things are pushed on us everyday. I know alot of nurses feel this way and hopefully it will change but until then..there is better out there. I for one, will most likely pay to get out of my contract in the next few months. It will be worth every penny. Best of luck in your move