TPE stopover possible with final destination KHH

coming back from the US, I have a 10 hour layover in TPE before boarding flight to KHH.
I have a JFRV and think about taking one of the free half days tours, offered by the
TaiwanTourismBureau. Theses tours are for transiting passengers.
My Q:
Would I be considered a transit passenger, if my final destination actually is in KHH ??
So, can I actual take the tour ??
If I take the tour, will I get a stamp in my passport ??
If yes, how to enter Taiwan, with my ARC or just with a landing Visa ??
If yes, can I re check-in in Taoyuan at all ?? (I don’t want to fly from Songshan)
Would it be a problem to have (maybe) 2 entry stamps and 1 exit stamp ALL on the same day ??
I just don’t try to fill my layover (CI cancelled my connection flight), but I want to avoid any
trouble if I (re)enter Taiwan in Kaohsiung …
Thanks very much.

10 hour layover??? For a 40 minute flight??? That is one strange travel booking… You could catch another flight or even take a train and be in KHH within a couple of hours. Maybe the result of reduced flights due to the opening of the High Speed Rail (HSR).

If you want to see Taipei, consider exiting at Taipei, spend the day, then catch the HSR to Kaohsiung. Why layover in Taipei for 10 hours when you can catch the HSR to KHH which in only an 1 1/2 ride… or could even fly on a different flight?

I had the 10 hour layover going the other way.
Went through customs and immigration at Kaohsuing, flew out at 7:30am then arrived at Taoyuan only to sit there for 10 hours waiting for the flight to LAX.
Luckly the travel agent threw in some free tickets to the Moore business lounge so i just sat in there drinking coffee, eating food and surfing the net the whole day.
If you are not in a hurry to go then the discount is worth the wait, from memory it was only US$765 KHH-LAX return.