If you are flexible, would you consider using your Qmiles to get to either Hong Kong, Singapore or Kuala Lumpur instead? Then you could do the final jump across to Manilla on one of the Asian loco's. Alternatively, you could take the one way award with QR and return with Air Asia (although they do not offer business calss as such, their long haul premium product is good value apparently).
Sorry to hear you're having problems. I generally use Emirates nowadays - award tickets attract much lower taxes than most other airlines and I've not had any major problems redeeming miles.
*Edit*
You say you've emailed QR with slow responses. Last time I redeemed Qmiles I did it online through the Qmiles website. Is this facility still available? I've always found their backroom staff in Doha to be a little bit lacking - you might even find that the tickets you initially wanted are actually available...