PRS

I have 259,579 AA points in my account and 134,617 in my wife's AA account. (I also have 138,000 BA Avios points.) Have never redeemed AA/BA points since usually book rewards with Aeroplan.

We want to book up to four economy seats from DEN to TPE (Taiwan) right after school finishes on Dec 21/22, returning on Jan 4 or 5, 2019. I know that AA does not operate flights to TPE so I cannot use the AA website to see award availability. But since there are JA connections via Hong Kong or Tokyo I thought I would be able to search on the BA website. However I do not get any results for DEN-TPE for Avios or even DEN-TPE paid ticket options on BA.com. I can find options DEN-HKG or DEN-Tokyo but mostly bus class. Also see 4 seats HKG-TPE on Cathay Pacific on Dec 20 or 23 for 4500 Avios+tax but not on Dec 21 or Dec 22.

Are there any valid award routings from DEN to TPE and, if so, is there a way for me to identify availability online? I don't have paid access to any award search tool but would consider it for this complicated routing if recommended. Or is my only option to call AA (or BA) and ask them to search for me? If DEN-TPE is not even a possible routing I would consider an option from a nearby departure and/or arrival city and then buy a separate connecting paid ticket.

Thanks!