Getting from Chiayi to Alishan through Fenqihu on a Sunday

I'll be arriving from Taipei to Chiayi on a Sunday morning by THSR (I'm flexible with times). I will also need to leave a bag in a hotel near the TRA Chiayi Station. I want to go to Alishan (without an overnight stay) with a stop in Fenqihu.

As far as I understand, it's quite hard to get tickets for the Alishan Forest Railway to Fenqihu (departing at 9 am and 10 am). The official website won't open, and I've read on the internet that if purchasing tickets at the counter, one must do it at least one day before the trip. So there are 2 other options: taking B line bus from TRA Chiayi station to Fenqihu (which only departs at 9:35 am and 12:05 pm) and then taking some bus from Fenqihu to Alishan. I assume taking the 12:05 bus is unreasonable because it will only arrive to Fenqihu at 2:00 pm (so I won't get to Alishan until 4 pm if I spend some time in Fenqihu), and the last bus from Alishan to Chiayi departs at 5:10 pm.

So my questions are:

• Am I missing any options?
• Should I not account for the the Alishan Forest Railway and should I just plan to take the 9:35 am bus?
• If I take the 9:35 am B-line bus to Fenqihu (which will supposedly arrive at 11:35), are there other options to get to Alishan before the other B-line bus arrives to Fenqihu at 2 pm?