The best way is to fly to Bangkok first and spend a day or two there. Test & Go is a simple enough program for everyone to follow.
Then just book a J ticket from BKK to wherever you want to go. There are plenty of good J class deal from BKK to Europe/US.

If you fly out from HK, Qatar is really $$$ even in March, but Turkish Airlines seems to have plenty of space available. They offer one stop flight to most of Europe/North America.

I will advise against separate tickets because rules keep on changing.

Carfield