This is our planning for a 2 week trip - any advice or comments?

Hi,
we are going to Taiwan for 2 weeks in may. These are my plans so far, do you think this is manageable? Also, there are side questions for some details included:

2 Days in Taipei

1 Day in Jioufen / Jiufen

1 Day Transfer to Taroko (Is it possible to rent a car in Jioufen or would we have to go back to Taipei? We wouldn’t want to drive in the big city if it is avoidable)
1 Day Taroko (Some advice on areas that are not so crowded?)
1 Day Taroko / Transfer to Dulan & Taitung (Can it be warm enough to bathe a bit in the sea in may?)

1 Day Dulan / Taitung (I’ve heard there are some hippie spirits there, just like in Goa? Can somebody confirm?)

2 Days Transfer to Kenting and Kenting

1 Day Kahosiung maybe? This is what I would cut out most likely if other places need more time.
1 Day Tainan because I read there is the best food

1 Day Transfer to Alishan
1 Day Alishan (Again here: We would prefer places that are not overloaded with tourists…?)

2 Days back to Taipei and Taipei

Any help would be very appreciated.

Speaking from my personal experience/preference I would do everything up to the Kenting bit, but then stay in Kenting at a nice place and chill out on the beach for some extra days. Skip Alishan (it’s a bit shite imho). Do a day in either Tainan or Kaohsiung, not both, you’ll be sick Taiwan cities by that point.