I would check all your flight options to see what is reasonable (and reasonably priced) when you are traveling to Israel. My husband and I went there last May, and ended up having two reasonably priced options in J out of NYC: Jordanian (which involved flying from JFK to Jordan, a short layover, then flying on to TLV), or Iberia (which involved flying from JFK to MAD, a longer layover -- and time in the new lounge -- and a flight with good seats to TLV). We chose Iberia, which worked out fine for our needs and budget-wise (and having the layover in the lounge in MAD gave us a chance to relax and recharge (I even got a decent nap in).
However, I fly with a manual wheelchair, which is different from what you are planning. And I speak Spanish fluently, which made the layover in MAD stress-free. Not sure what it would have been like otherwise.