For Mürren, you might look at Chalet Fontana for a good budget option. This has been one of Rick’s recommendations for at least 20 years. We stayed there on 3 separate trips some years ago, before migrating to large apartments with family members. It is a B and B with shared bathroom, and no Mountain View’s from the rooms, but walk outside and wow! A nice breakfast with the other guests is included.
http://www.ferntree.ch/chalet/fontana_summer.htm
Some of the rooms are rented through Air BnB and according to their calendar, Room #1 is available in late September. That is the room I stayed in our first time there, before we started taking the ground floor apartment.
For Wengen, I was going to suggest hotel Bären, which is about 4 levels up in terms of amenities and views. When we last stayed with them, their in-house restaurant was regarded as the best in Wengen, and half-board there was (and still is) a bargain. We would see Therese, the hostess, heading out after breakfast each day to buy produce, eggs, cheese and butter from the local farms to serve at breakfast and dinner. That local fresh butter was so good—- so much better than anything one can buy in packages at the store. And they grow herbs and some salad greens in their own garden by the chalet.
But they do not offer single rooms on the internet booking. You might contact them and ask, as things are more flexible in late September. If not, you could at least enjoy dinner there while staying elsewhere.