This is a very fine point, but RTW fares did not allow back-tracking. Your routing on the RTW should really be DFW-LAX-HKG-CDG-DFW .. with a second ticket that is totally separate for HKG-BKK-HKG (yes on CX). I did ORD-LHR-SIN-HKG-SFO-STL-ORD with a 'side trip' to China from HKG .. but it was on a separate ticket to avoid the backtracking no-no.
Not sure this is a huge issue ... but normally the staff that book a RTW are sticklers for details. Thats why Australia is a bit of an anomoly on a RTW on some airlines (allowing SIN-SYD-MEL-SIN-LAX vs SIN-SYD-MEL-LAX where no 'reverse direction' is involved) and I think like UAL and SQ surcharge because of that. Not sure how AA/CX would feel. AND the agents may be rolling the RTW and HKG-BKK-HKG into one 'price'.
Just thought you should no about the no-no dreaded back-track on a RTW.
JR