Itinerary Weather Considerations

You could optimize the route a little by visiting Luzern after Grindelwald/Mürren, on your way to Appenzell. It will break what is otherwise a longish train ride and it allows you to use the scenic Luzern-Interlaken express and the Voralpen express from Luzern to St Gallen.

So, you would head from Zürich to Lugano.
Also, I am not sure you need a contingency day in Zürich. I would rather add a night in Grindelwald instead.

And regarding Lausanne, since your focus is "small villages", you could also stay in the smaller towns further east along the lake (Vevey, Montreux).

As for weather, I am not sure shifting things makes a big difference. If you move Luzern to the end, you already shift things by three days.

If you want to have the best chance of good weather, visit the places open to the northwest first. Almost certainly that time of year if you get stormy weather, it will come through from the North Atlantic. The BO is on the front of the range facing nnw, and as wet air hits those mountains and starts to rise it will disproportionally dump more precipitation. The Lauterbrunnen area is a bit of a storm magnet and seems to nearly conjure up it's own weather.

Pontresino by contrast is deeper in the range and farther south and east. It should have a better chance of better weather later in the fall, storms not strong enough to penetrate to it maybe, or the moisture already wrung out by the front range.

But, but, but! You're only looking at a marginal difference, particularly in very early fall when you are travelling. You've got a great chance of decent weather overall in your travel window. If you want to absolutely optimize your chances of fine weather throughout, then change the order of your itinerary. But you could also not sweat it as you are already nearly perfectly set up for good weather anyway.

And anyway, if it rains a couple of days on your visit to Switzerland that's certainly something to experience too. Switzerland is green for a reason! And as the Scando's say there's not bad weather only the wrong clothing. Some of my most memorably days in the Alps have been poor weather. It makes you pull your interested eye close than the towering peaks, and you notice that everything within 50 feet of you is painfully charming and cozy, almost glowing with alpine character. :)

One more thing to consider, in late September you could still be in warm weather thundershower season if it stays warm. So you could ostensibly get hard afternoon rains early in your trip and mild clear weather later. No way of knowing - you could shift things around only to run into more rain early on. Weather gonna weather :)

Thank you so much for your comments and suggestions. They were very helpful and we are going to tweak our itinerary as a result.