I actually did do a bit of research on flying to Yangon, RGN. I didn't find anything recent.
I looked at the threads you suggested and maybe OZ one way and NH the other will be the best bets. I can get there in 3 flight segments with either of those airlines with about 26-28 hours total travel time.
MCI-SFO-ICN-RGN on OZ going over is 28h10m, limited to 3 days a week
RGN-NRT-ORD-MCI on NH coming home is 27h13m
RGN-ICN-ORD-MCI on OZ coming home is 25h13m, 3 days a week, but no QS seats