Thanks for all of this great input, folks.
hadn't realized that I should check the BR and possibly the CX sites for fares that third party sites don't supply. I'll do so shortly. Great tip! I've flown both before in J and agree that they're great.
exwannabe, good question why I'm looking at a Skyteam carrier. The answer is a bit idiosyncratic (but hopefully not idiotic

) and multi-faceted. For one thing, I'm kind of burned out on loyalty to US carriers' deteriorating FF programs and services (including but not limited to the new basic economy "option" that UA in particular is imposing on its domestic flights) and am mainly accumulating miles and points through credit card sign-ups and spending. For another, cost really is a factor here and thus far the Skyteam carriers and the mainland Chinese ones in particular offer the best options. Yet another is that I already have lifetime status on AA and UA. Finally, I've begun to accumulate miles on Korean, so flying Skyteam gets me some potentially useful miles anyway.