I'm still not sure you're getting the distinction between "reservations" and "ticketing". A OWE can only be ticketed on one carrier's stock. It is the reservations that I make directly with each operating carrier. That doesn't affect whose stock the ticket is on, so if the carrier's miles for upgrade policy depends on the ticket stock of the underlying ticket then that may affect your choice of which carrier you use to issue it.

Note, of course, that if you do a reroute/reissue after starting your trip then the you can change ticket stock at this point. For example, many of my OWEs have started in CAI; some were originally issued on BA stock and some on AA, but whenever they were reissued at HKG the reissued ticket would be on CX stock. Most of my more recent tickets have been AONE3s so the question of upgrades hasn't arisen, but I have upgraded CX segments using AsiaMiles on DONE3s and I don't recall the question of whose stock the ticket was on being raised, although I'm not sure whether I have ever upgraded a CX segment on BA or AA stock.