I'd lean towards a faulty master cylinder rather than brake booster, given that it's some remanufactured Chinese part. It sounds like the brake booster is working normally if vacuum is present and you checked the check valve. Perhaps look into a new master cylinder at
RockAuto. I'd imagine Beck/Arnley or Cardone Select to be of satisfactory quality. If you order from RockAuto, be sure to
use a 5% discount code.
I'm still unsure of the cause though - I've never experienced symptoms of either a failing master cylinder or brake booster, so perhaps you should try to get a second opinion somewhere.