yes, you can apply for reciprocity and transfer your cert over to NJ. They usually make you take a recert class and take a test though
sorry, but no, wrong wrong wrong!!! absolutely 100% wrong, and completely unnecessary work.
8:40A-7.3 subsection (a) says "A person validly certified as an EMT-Basic by the NREMT, the State of New York or any member state of the Atlantic EMS Council (currently Delaware, the District of Columbia, Maryland, Pennsylvania, Virginia and West Virginia) shall have status as an EMT-Basic. No further testing shall be required, and the EMT-Basic certification card issued by the out-of-State certifying agency shall be valid for the purpose of proof of EMT-Basic certification."
http://www.state.nj.us/health/ems/documents/njac840ar.pdf
So as long as you keep you NYS EMT valid, you can work in NJ with a NYS EMT patch on your shoulder (assuming your agency will accept it, most will or give you time to transfer).
Now that we cleared that up, the follow up question is 1) where do you want to work, and how far of a commute do you want 2) do you want busy urban, busy suburban, semi busy suburban, rural, or something else 3) are you looking for days, nights, weekends, etc 4) do you want a 100% paid agency, or combination paid and volunteer system and 5) do you want 100% 911, mostly 911 with a few transports, mostly transports with a few 911s or a little of everything?
There are many places that have paid/per diem staff in the NYC metro area, ranging from GWB area in bergen county all the way down to Perth Amboy by the Outerbridge crossing. Some pay better than others, some are busier than others, and some areas are better than others. But it would also depends on where you are coming from, to limit your commute.
let me know, I might be able to point you in a good direction as to where to start.