Oberland and Lucerne questions

The Lauterbrunnen valley is very small, these villages are not far from one another. There is no need to be staying in Mürren to go up the Schilthorn - from Wengen it takes only 1 hour and 14 min.

If you feel that you would rather be staying in Wengen in bad weather then I would go ahead and stay there, you will still be able to access the whole area very easily. I really like Wengen and think it is a great choice, but I don't quite understand the connection to bad weather?

Pilatus: I would skip the boat unless you particularly want a a boat ride so you can maximize your time on the mountain. We took a train to Alpnachstad, then the cog wheel train up (cable car was not running in October). There are many hikes you can do once atop. No need for a tour guide, everything is easy and well marked.
I went to Murren and not Wengen, but I don't see how Wengen would be any better in bad weather (which should be less likely in June than it was in October). We had one day of rain and went to Schilthorn (no visibility but it was fun to see snow atop a mountain) and used a sauna.
For the extra night, make a detailed list before deciding. I had four nights in Murren and would change nothing, though I certainly could have spent longer if I had the time. I had two nights in Lucern, and would have loved to have at least one more day.

I'll be the contrarian here. While I understand the desire to stay at the higher elevations, to me you cannot compare the views from the valley floor throughout the day and especially at sunset. Unless being able to get to a trailhead 5 minutes from your room is the #1 priority I cannot see a benefit of staying "up top". My 2-cents.

seeing the "glow" of the mountains at sunset from Mürren is to me incomparable

Murren is your spot, definitely.

My comment is the trip from the Black Forest down to Murren. You mention lunch in Basel. OK, if there is something you particularly want to see in Basel. What we did, and loved, was stopping in Bern for lunch. Bern (at least the old city, which is where the train station is) is a much less industrial, more authentically old city (it has never been destroyed by fire or war, and so the buildings are original from the 15th century). Its traffic free, and easy to stroll from one end of the old town (the station) to the other (the bear zoo). Along the way are the Zytglogge (think giant cuckoo clock that goes off every 15 minutes), and plenty of shops and restaurants. You don't say exactly where in the Black Forest you are starting from, but if we assume Freiburg, its about 2 hours by either car or train (although the train trip, admittedly, does connect in Basel).