I prefer the local trains for reasons Melmnq8 gives - cars are often largely empty and you need no reservations like on the official BE to take them - with a ticket just hop on and off anywhere you like.

Thank you all for the replies. Now that the overall itinerary is somewhat fixed, we have to plan each day's activities, with backup plans in case the weather does not cooperate. I will update this post soon.

By the way, is there enough daylight in Switzerland late into the evening during June? We can pack more into a day if that's the case.

Best Regards