JFK-LHR or LHR-JFK is still pretty easy to clear.
AA141 on Sunday 6/26: upgrade to J using SWU cleared at boarding (but missed the flight #anotherstory)
AA107 on Monday 6/27: upgrade cleared before boarding
AA 104 (JFK-LHR) on 8/17: received the notification on EF on 6/29, and the AA exp agent promptly handled it over the phone.