I'm looking to book AA104 as an LY codeshare (LY8053) as part of a larger JFK-LHR-TLV-JFK itinerary. I found an O-class itinerary (OL3USA3M) which prices at about $1100 r/t.

Previously (and for EQM and bonuses this would have been far preferable) I know it was possible to book this kind of itinerary as an AA codeshare. But since the FAA downgraded Israel's airport rating, AA no longer puts their codes on LY flights. It also doesn't seem to be possible to find the itinerary on AA.com using the "all airlines", by schedule and "show 50 flights" options.

Is it possible to book this itinerary on AA.com?

Does the LY fare JFK-(LHR)-TLV-JFK allow an AA flight for the JFK-LHR portion or is it only possible with AA104 coded as an LY flight?

Alternatively, is there a published AA fare JFK-TLV-JFK which would allow one to fly JFK-LHR on AA and then LHR-TLV-JFK on LY? I am wondering whether AA is now reluctant (after the JBA with BA) to allow a JFK-LHR-TLV-JFK fare which would include LY rather than BA.

Finally, if I must buy the LY coded ticket, can I still use my AA elite status to reserve the exit row on the JFK-LHR portion?