Does it have to be a trans-atlantic segment? I did manage to find an AA codeshare for HKG-DPS-HKG. Would that help the situation?

Just saw jkirsch's comment: I think I'll give AA a buzz this afternoon to see whether they will accept codeshares. If not, I think CX is the next best option. I've seen on here somewhere that BA does charge incredibly high surcharges?! Not too sure so would be great to have some advice which OW airline I should approach to book and issue my DONE5.