Try searching JFK-TPE and TPE-DPS separately on Delta.com -- for some reason Delta.com often doesn't suggest connections with China Airlines, but you can see the individual segments. (Make sure you account for the fact that you land a day after you depart in figuring out the right connecting flight option, of course.)

If you can find segments that would work as a connection, I have had luck getting a phone agent to combine China Airlines flights that weren't coming up as a connection on the website. Be very specific with the agents which flights you found on the website and ask them to see if they can combine them into a single itinerary. (But that was also Diamond Medallion line agents -- if you don't have any status with Delta and are calling the general line, you may need to call multiple times before you find someone competent enough to do this. Keep at it. It can be done.)

China Eastern and China Southern may be options, but those airlines generally get pretty bad reviews -- I would make an effort to avoid them if at all possible.

Korean may be an option but generally speaking they only release 1 business class award seat per flight to Delta right now. It is possible that may change once the Delta-Korean JV goes into effect, but that may not happen for a while so I wouldn't recommend waiting for that unless you have no other choice. But, if you end up booking China Eastern or China Southern because you can't find any other option, and then Korean appears later, it would be worth paying the change fee to change to Korean. (If you're PM or DM there would be no change fee anyway.)