Thanks for all the replies. I had thought I had read on a previous thread (possibly even one I started) that I could fly 4 segments on a 20-segment paper ticket and get it reissued as an electronic ticket by the originally issuing airline, and--assuming I wasn't re-routing--not be charged for that. Is that correct? Assuming it is, I thought that maybe I could get another airline (other than the originally issuing one) to reissue the ticket.

I also had thought based on christep's post that I could have my originally issued AA DONE5 reissued by BA: "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." My thought was that once it's reissued in that fashion I would be able to upgrade a BA segment. Maybe the part I'm getting hung up on is whether the gating factor for upgrades is who sells the ticket, rather than whose ticket stock the ticket is on--which may be the same, but need not be in the case of a ticket reissue. But, based on the reasons that Viajero and others have said, maybe this doesn't work. Oh well.