Round-trip awards allow you to have 1 stopover and one open-jaw. What you're after is 2 stopovers (one in each direction) which is not allowed on a single award. You can also have (basically) unlimited breaks of less than 24 hours which do not count as a stopover.

So your options are :
1. Book it at the higher rate.
2. Reduce one of your stops in TPE to be less than 24 hours, at which point it's just a connection, not a stopover.
3. Book the award flight SFO -> TPE -> HKG, TPE -> SFO (which is a stopover in TPE on the way out, and then an open-jaw on the way back) and then book a separate paid/award flight HKG->TPE.

Option 3 is probably how option 1 is pricing out - the extra miles being for the additional one-way HKG->TPE