Definitely the F. Especially if it's on the A380 for the TG portion.
Just know there is no caviar on BKK - NRT (or at least there was when I flew NRT - BKK last year). I did get a Rimowa amenity kit though and Dom.
Does United domestic F not qualify as F for AV? If it does have you looked into routing via ORD or even IAH and then seeing if there is UA F availability?
Another option to consider is OZ F to SEA which is getting Suites for some period of time - though I don't believe TG / OZ have any F to ICN so that might not work with AV