I did a quick check on a few of the BA 747s and see the ones I checked are all on long haul routes. So your $6000 plus fare will be about right.

If she is eligible for any airline discounts based on your employment, you may want to check if DL have any ID agreements that give discounts on OAL first class fares. I would doubt it, but there may be an old ID75 or ID50 agreement that covers first class and is still available. I see you already asked about buddy passes, and although I have no idea about their pass policy, even if you could get one for her, the chance of an upgrade is probably close to zero.

Depending on your location and her holiday plans, you may want to look at one or two of the far east airlines. For instance China Airlines from TPE to HAN is around $580 (OW) in business class, and I think they have some of their biz class upstairs. Korean from ICN to MNL is around $948 (OW) in first class. There will be several others, but absent any positive info on this site, you will need to spend a considerable number of hours exploring what and where.

Good luck. Lee