Welcome to My Swiss Alps -
The forum is quite busy these days. Sorry it took so long to answer.
You obviously know a lot about the country.
I agree that the Tamina Schlucht is a nice idea. The restaurant there is not too bad, either. The wine from the local vineyard (":Highest Vineyard in Switzerland") is rather disappointing, unless they happen to have an Auslese.
However, I wonder if some more ordinary might actually work better as a way to give an impression of Switzerlnd. Thus, perhaps a regular tourist destination, such as Luzern, as you suggest, is probaly a good idea..
Or, how about the Emmental?
There are good links in this thread:
I did not have time to carefully review your post today, but, that will give you a start. Peterli, who knows the Suisse Romande very well may wish to jump in if catches this.
Snowman, knowledgeable in the French region but also the rest of Switzerland might help as well.
The Hotel au Sauvage in Fribourg meets your definition of a splurge, but not terribly overpriced. . Right on the language border, though, actually, mostly French. I stay there regularly.