About the only thing I would have done differently is to declare an emergency.
The recent thinking, under U.S. regs anyway, is that it gives you carte blanche with whatever decisions you make as PIC. And it's CYA for stuff like landing back at JFK without getting re-dispatched.
I understand the CYA stuff...but seriously, if someone would give them a hard time for returning to JFK without getting re-dispatched, they need to get their heads checked. Decades ago I was taught that declaring an emergency means "grave and imminent danger to the aircraft or lives", and that tying up scarce resources is not a good practice if there is no such grave and imminent danger. But maybe I'm naive.