as long as you stay with the rules (separately, and parallely). you have the full right to fly whichever way you like.
this should not be anything different from using 2 restricted fare tickets in paralell.

the RTW is so comlicated (for the computer/IT) that i can assure you they will not be able to track it until we are in the blade runner age:_)

in fact, since u haev 2 tickets, why not consider some free side trip in these continents? (e.g. in NA with your ex-bkk tkt)