There's usually a fair number of available positions for this sort of thing out there; not a -lot-, but -some-, and the program quality is variable. Every year a few spots go unfilled, some people quit, some are fired, and some transfer or change residencies altogether. If you have a good strong reason, the kind everyone understands, then transferring is not really frowned upon -- so long as the "new"/receiving institution feels like you're going to be stable until they can graduate you.
Your PD can really be a major help. There is a PD contact list available to PD's, and that could turn out to be the only thing you need. I know several who went through their PD and received several leads from them and several phone calls on their behalf, and it seemed to go fairly quickly and smoothly (had interviews within weeks and a new position lined up within a couple months). With rare exception, programs want you to start July 1st, as previously indicated.