Seriously. Maybe Florida just has a shortage of mental health patients... sunshine and all, but elsewhere psych nurses with a psychology background would be offered a position with the red carpet rolled out.
Places in this area actively looking for psychiatric mental health nurses:
Presbyterian/Texas Health Resources
DSHS (Terrell State Hospital, Kerrville State Hospital, Vernon State Hospital... etc)
So, chances are that you are either working in a saturated market (nurses like sunshine, beaches, and Jimmy Buffet), or you're knocking on the wrong doors. I would suggest knocking on the doors of the state, county, city mental health services. If they're anything like Texas, they will be more than happy to have you work for them. Caveat: the salaries may be lower than what you're expecting, but you're looking for that golden year of service, not a life-long commitment to civil service.