Another airline cannot 'take over' an itinerary which AA has set up for you for the original reissue.

So to make things easier in that you don't hold double bookings and such, CANCEL your reissue with AA and rebook the entire itinerary with another Oneworld carrier - hopefully one that has at least a long haul flight in your itinerary. I find BA and CX very good with reissues. Yes both BA and CX seem to have less problems reissuing international tickets. Maybe its because they have hardly/no domestic flights.