Have not done it. It is an old trade route and a great hike. Can't help with details. For some reason, my friends tend to start at the Kandersteg end.
Did you check on Switzerland Mobility? I'm sure it would be there. Let us know if you cannot find it.
I've not stopped there. I have always thought it was a special location and worth a visit in its own right, but never fit it into our plans.
Your time plan is reasonable, but getting the taxi could be a delay for you. That could make it a bit rushed. I don't recall a taxi line at Flüelen station, and we have been through there many times. Were not looking for one, however.
Judging the appeal of scenery is an inaccurate and potentially trouble some practice.
My opinion is that what you can see from the shore is not much different from what you can see from the boat. If you were taking schoolkids for a history lesson, you would want to spend time there.
I have done my walking on the other side, as noted previously in :
We did walk from Morschach to Sisikon one time, well above the lake, and the views generally did not include the lake. I looked back at those, and nothing causes me to want to post the few that I took.
The view from Brunnen is worth some time, in my opinion.
I have attached three images of the eastern shoreline, taken from more or less above Bauen, and included a full res crop of the Tellskapelle location. Images 1, 2, and 3 overlap. The include Sisikon, Tellskappelle and go as far south as Flüelen in the haze. I considered building a panorama, but would have had to do too much work in Photoshop to resize the images.
A photo from the pier at Brunnen shows the eastern shore line somewhat; there is one profile recognizable in several images.
The entire southern end of the lake is sort of visible in one image in the Swiss Path link I noted above.
Two other attached images picked up on the internet may be helpful.
Personally, I'd stay on the boat, look at the scenery from the boat, and include Tellskapelle in another trip, after I had a look at what is there. And, it is considerably less rushed to do it that way. But, at the level of detail we are discussing, my opinion may not be relevant.
I also found some more images taken from the Bergsonne, which I shall post at another time.