I dont hve a clue about the ticketing onto another carrier bit, but had seen this advice on FT (think it was Guy Betsy) - 'politely but firmly ask them to put it in the system and it'll go through' - worked the one time i had a problem (using a stopover allowance for a transit) - and they didn't even bat an eyelid the other time i used the 'stopover' for a transit.
BTW OP, since you're stopping over in TPE, and only transiting KUL, you could do TPE-oHKG-oSIN-oCMB on CX all the way..MH would be narrowbodies for this routing, while CX will likely have the new regional biz seats...or, buy a an exTPE discounted biz fare to SIN/CMB..
FWIW (OT), i've redeemed for: SFO-xHKG-oDEL-xKUL-oSIN-xHKG-SFO//SJU-xDFW-SFO
I got a call back a day later that 'ticketing says this is invalid as you've returned to SFO, the origin', to which i showed an earlier redemption:
LAX-oLIM-oEZE//GRU-xLIM-oLAX-oSFO-LAX
and the apologetic agent accepted that 'return to origin and then travel beyond is fine..will remind ticketing'