Why not try to book two tickets?

1. Using TPE as stopover, you book the 1st tix (say Tokyo).

2. Work with the 1st tix then find the 2nd intra-Asia tix departing from TPE (i.e nested tix). It's very easy to fly to HK & Hangzhou from TPE.

I doubt these two tickets would cost you more than $6K. Good luck!