Have you explored other LH F options such as:
ATL-IAD/ORD/EWR-FRA
or
ATL-CLT (on US)-MUC
Keep in mind that TG flies to BKK from LHR, ZRH, MUC, FRA, CDG, and MAD.
Also, sometimes LH operates ATL with a 2-cabin aircraft, so it might not even be a possibility to go in F.