Here are some of the airline/cabin/routes worth considering:

1. ANA F - very hard to find seats in F most of the time (they do exist), but well worth it if you can find one. Ex-NRT is better catering-wise than departing overseas, but general catering quality heads and shoulders above most other airlines, and service is beyond reproach as well. NRT lounge has its charms, but not really in the same league with the more interesting Star lounges such as LH FRA or TG BKK.

2. LX F - easier to find seats in F depending on the route (Asian routes, especially NRT/PVG are the easiest in my experience) and one of the best F experiences in Star. ZRH lounge not as good as FRA/MUC but 1. still possible to use FRA/MUC lounges if you connect to LX F same day, and 2. onboard experience quickly makes you forget any such minor differences in lounges. Catering should be excellent out of most stations (except PVG that I've heard negative reports)

3. TG flights in the 77W product (BKK-NRT/CDG) - very impressive hard product, and TG seems to have gotten their act together a little better of late. I had a phenomenal flight last month in F on NRT-BKK with excellent hard product, decent catering and excellent service. Ground services departing from/arriving at BKK very impressive, particularly the former with their 60-minute full body massage.

4. OZ F flights (ICN-FRA/JFK/LAX) - have only flown short-haul OZ F myself, but collective experiences of FTers have been overwhelmingly positive in terms of soft product. Some quirks with hard product (i.e. 747 F seat retaining a slight incline at full bed position) but the catering and service should be fantastic. Lounge at ICN nothing too exciting in my opinion, though others seem to like it more.

None of the US airlines really qualify (either 2-class or UA F), SQ is just impossible to find seats in longhaul F, and I can't think of other airlines that have a noteworthy int'l F experience...

LH F product is really too dated to qualify as a luxurious F experience these days. LX F seat considerably better (both old and new). If you want to experience FRA FCT (best lounge in all of Star, IMO) then just connect to an LX flight in F on the same day instead.