I see four oneworld options between New York and Tel Aviv.

The best by far is BA via a smooth connection through LHR's new T5, though I can understand why this might not be your preferred option as an AAdvantage member (but oneworld is far, far more than just AA - thankfully!).

Second-best option is flying Iberia through Madrid, which offers a fairly smooth connection but only an A320 on the leg to TLV.

Then there's the option of AA to Heathrow, connecting to BA, though this involves changing terminals, which is a bit of a hassle.

Finally, you can fly Royal Jordanian nonstop from New York to Amman, connecting to the short hop to TLV.