No I will not risk it. Separate tickets are tricky these days and they are not even partners.
So I will book an earlier HKG-TPE ticket and expect to go through immigration and custom at TPE. JX uses terminal two for US flights, so you need to transfer from T1 to T2 at TPE. It is not difficult but you need to add about 15 to 20 minutes to your transit time.
JX has two daily flights from HKG to TPE, and while I know that you will have a super long layover at TPE if you book JX, I will do it.
Carfield