The only BMED-esque route on the BA mainline network is Tripoli, and this won't be transferred over as;
1) BA make a lot of money on this route
2) BMED aircraft can't handle the club volume on this route (50+)
3) BA shorthaul crew can operate the service on an Airbus, non-stop and within the same day.
The rest of the middle east/africa/asia is doing fine for BA mainline. For reasons that Sonic Cruiser has mentioned above, BA are not very interested in BMED routes, as long as BMED continues to fly most of them. The only route with potential for transfer at the moment is THR, as BMED aircraft aren't ideal and there is a possibility of using the longhaul 767 either direct, or as in the past, via LCA.