Want to get to Checheng early from Taipei; are HSR and TRA almost 4 hours?

I did a quick comparison of train timetables and it appears that both the HSR and regular train take almost the same duration, because the firsst HSR is around 6.30 am. In addition, if I take the HSR, I still have to change trains between taichung and xinwuri and ershui stating and the walking negates the time gained from using a HSR.

Is my understanding of the timetables correct? Does anyone know any better way?

So regardless of whether I take the HSR of TRA railway from Taipei, the earliest I can reach checheng station is at 10.10am?

I am not sure if the day of travel makes a difference, but if you do it on a saturday, the there is a train leaving from Ershui to Checheng starts at 8:00 and gets there at 8:50AM. So the rest is whether or not you can get to Ershui before 8AM.

There are also trains leave Ershui at 06:02 and 04:45 on weekends, not sure how you are going to make those.