Cathay Pacific Asia Miles - Can someone please help me with this multi-country itinerary?

Ok, I'm starting to make myself nuts trying to figure out this itinerary. I've never traveled to this part of the world or with Cathay, and I need some expert help. I have a multi-country trip for business, and here is what I'm trying to do.

I can book paid business class. ORD-HKK, for meeting in HKK on Oct 15. Need to get to Tainan for meeting on Oct 16. (I have not been able to find any flights to Tainan.)

Taipei for meetings Oct 17-18. KUL for meetings on the 19th, but I'm thinking it might not be possible to get from Taiwan to KUL in that time frame, and may have to delay meetings to Oct 22.

Singapore for meetings either Oct 22 or 23 depending on when I get to KUL. After meetings in Singapore, then return to the USA.

Currently, the most trouble I'm having is how to get from HKK to Tainan and then to Taipei. I'm not finding flights on any airline. I don't want to drive between the cities, and I don't know what to do. I'm also not sure of the flight schedules and timing to get to each of these cities in support of the meeting dates.

Any help would be very much appreciated.

Thank you.

I assume you mean HKG (Hong Kong), not HKK (somewhere in new zealand)

In which case you can fly from HKG to KHH and take a taxi or hotel car from KHH airport up to Tainan.

From Tainan to Taipei is easy on the high speed train.

TPE to KUL should be easy, direct or via HKG / SIN.

KUL to SIN also easy

Dragonair operates many flights from HKG--KHH (Kaohsiung) daily. I'm sure they suit you best!

A train service from KHH to Tainan only costs you around 1 hour, or high-speed rail with just less than 20 mins.

TPE --> KUL you may choose CX via HKG or direct flight.
via Singapore not worth it unless you like taking SIN--KUL such short flights..

Currently, the most trouble I'm having is how to get from HKK to Tainan and then to Taipei. I'm not finding flights on any airline. I don't want to drive between the cities, and I don't know what to do. I'm also not sure of the flight schedules and timing to get to each of these cities in support of the meeting dates.

As others have said, to go to Tainan, fly to KHH (Kaohsiung) first, where KA (Dragonair, treat is more or less like CX's Eagle) flies 6 times a day. Then, you can take the metro either to Kaohsiung Main Station to transfer to the TRA (normal train) or to Zuoying to transfer to the THSR (high-speed rail). Both TRA and THSR goes to Tainan, but the former goes to downtown whereas the latter does not (however, there are local trains and free shuttle buses to downtown). THSR has English signs and English-speaking staff everwhere, while TRA, though has English signs, might present more problems to travellers who reads no Chinese.

From Tainan to Taipei, THSR is your best option, which takes you to downtown Taipei in about 1 hour.