Imo, the commute is just tooooooo brutal! I don't think I could emphasize enough.
Your work times would run you smack into rush hour no matter whether LI to NJ, or NJ to LI.
LI highways at rush hour are an absolute *crawl* and then you've got either the bridges or tunnel to Manhattan
AND the bridge or tunnels to NJ. DOING THIS DURING RUSH HOUR IS SIMPLY INSANE!
Probably a two hour commute, and add 30 minutes just to be sure you'd always be on time, given the vageries of traffic. Even then, an accident in one of the tunnels would do you in; and, you'd likely not make it during a snow storm.
I suggest, one of you take a cheap studio or share near one of your jobs, and live separately during the work week, until you find a job on LI or NYC.
Remember, separation makes the heart grow fonder!
If not the above suggestion, then probably some place very near either the Triborough Bride or the George Washington Bridge. Astoria, Queens or Teaneck, NJ. Since you have the rolling shifts (hospital worker/tech/doctor?) probably Teaneck.
For the wife, once thru Manhattan she w/b driving opposite rush hour traffic; and you w/h an easier time making it to Elizabeth given your scheduling!