Lucky you. I wish I could put together 3 weeks in Switzerland and at just the right time of year.
I'm still a bit confused by your descriptions, so, could you please tell us what dates you are likely to arrive in and depart from Switzerland?
If you are visiting the high alpine areas that you mention, you should push them to the earliest part of your trip. By the time you get into October, although it is generally still nice at high altitudes, weather can become a bit chancy. Would you consider putting Paris at the end of your trip?
Just for perspective...there was snow in August 2017 at Männlichen , above Wengen. Unusual, but not unknown.
So, for planning purposes, perhaps it would be best to think about going to Basel as soon as possible after Paris. And, both Luzern and Bern are only a short ride further from Basel, as is Zürich, so you might be able to skip Basel if you choose to. At that time of year, hotels are generally not full, so you can likely adjust reservations, unless you booked in some way that does not allow cancellations. Not surprisngly, different people seek different things in Switzerland. So, When we look at an itinerary, we think about these things first , then select locations, considering available time and transportation options -
1.- Scenic beauty, majestic mountains,
2.-Old towns, as in St. Gallen, but not only there,
3.-Hiking or walking, near major cities, in the Alps, or in the rural and farming regions - it is bit early for skiing ;-),
4.- Museums and cultural experiences,
S.- Scenic train rides,
6.- Good food and fine restaurants,
7.- Experiencing the (rural) countryside in places that tourists don't overload.
9.- Places your Swiss ancestors (if any) came from.
Can you give us some guidance on those items and perhaps a general idea of their their priority before we offer further comments?
Switzerland has a lot...perhaps too much ... of all of those things, which requires choices. ;-(
Perhaps you have seen this, since you have noted a reasonably adequate time in Wengen...;-)
If you want to do some thinking about what makes sense, purely from a scheduling point of view, these two links can be helpful. A map is always useful -
In the map link, use the menus. Oddly enough, "Gastronomy" includes places to sleep.
Note the proximity of Bern, Luzern, and Zürich to Basel.
And, for schedules, to see just how often the trains run-
The first page is full of useful information...please check it out before you dive into the timetable.
As I read your comments, I see that you have some clear ideas of places that you want to see. However, I'm not sure why you have selected them. You seem quite well informed. Could you give us some clues? By any chance, do you speak any of the 4 Swiss national languages? None are needed, English works well, but Ann Arbor has a lot of well educated people. ;-)
Random photos attached