It would be a good idea to work on getting your medic while waiting for a call. I know that LaGuardia, Suffolk CC have degree programs, and I think that BMCC does as well. You could also go the cert route. I may be a little out of the loop, but IIRC NY Methodist runs medic programs in BK and the Bronx. They had classes that run 1800-2200 M-Th, and 8 hour classes twice weekly, I think M/W.
A medic program may cost 6-7k, but you can easily make it back in the first year. Just get a loan if you have to, or establish a payment schedule with the school, or some combination of the two.
I was lucky, as I was working for NS-LIJ as an EMT while going through medic school, making 20/hr, plus 2/hr night diff. The medic promotion bumped me to 22/hr, then 25 after six months, and then 30/hr after a year. There was that salary bump, more OT, and availability of per diem work at other hospitals making 25/hr or more. That's how you make it back. If you work in the privates making 10/hr, the medic upgrade will bump you to 20/hr or more. Every $.50/hr is a little more than $1,000/yr. So, that's a 20k/yr bump, gross.
Having your medic will make it all the easier to get into FDNY EMS. There was and will always be turnover. It's a fun job, but the constant harrassment by conditions bosses, mandations, lousy pay, etc wears many down. The hospitals always get ex FDNY EMS employees. They start out per diem, then go FT when they see how much better it is on the other side.
The FF's don't even make a liveable wage in the FDNY, so the EMT's and medics are even more screwed. At least at FDNY the FF's can do swaps and basically work a 24/72, or work every other day for a month and have a month or more off. At FDNY EMS, they work 8 hour shifts, five days a week, with an extra day off every third week or so. Google FDNY EMS platoon schedule to see for yourself. Couple that with mandations, and there's little time to work side jobs. At least the FF's have enough time off to work a second FT job if they want. Quite a few work for the hospitals as EMT's, medics, and nurses.
I think that, as a new EMT you may qualify for food stamps. No joke. I heard the same for NYPD a few years ago before they had their most recent contract negotiation, finally giving them a liveable wage.