I've run into this problem, where in certain markets they have the option for purchasing a Q class ticket at times, but then at other times remove the option. Or in some cases they never have it, but only allow the selection of a restricted (usually V or W) or non-restricted (full Y). A couple tricks to get around this:
If it only shows V or W for the flights you want, find a flight where V/W are sold out and it will give you a Q fare. Book the ticket, then call up the local office and change it to the flight you want. Of course you need to check first that the Q fare is changeable without a fee, and if booking on a different date, that the date falls within the same fare classification for the date you want to change it to.
At times I had some luck in using the multi-city option to pull up a Q fare where selecting a normal round-trip just pulled up a V/W fare.
Buying ex-MNL tickets is difficult with many airlines, not just TG. Even with travel agencies, they typically want to be paid in cash only. I guess there's a lot of credit card fraud in the Philippines and the airlines typically have lots of restrictions in place to try to protect themselves.