using QF credit for Europe flight + AA challenge

[svstrider]

I am looking for help re my dilemma. I have about $900 credit with QF that I must use by 23 Nov. My partner and I want to travel to Paris, business class. I have 145000 points & she has 76000 FF points. Ideally we want to go vis HK on the way over and Singapore on the way back vis One world airlines. I want to obtain the AA Platinum challenge.

Any ideas how I get the cheapest business fare??
Thanks
Paul