Sep 8, 2019 - 10:46 PM
As you noted, the end of September is a bit of an awkward time, but the Gleckstein, Rotstock and Gspaltenhorn huts are open until the end of September. The Gleckstein is a popular destination for both day and overnight trippers coming from Grindelwald and you would probably have to book ahead if you wanted to stay overnight. I've been past the Rotstock, but haven't stayed there, but it is a good starting point if you want to cross the Sefinenfurrge Pass into the Kiental Valley down to Griesalp. That is a lovely hike - in good weather. Altenatively, after you cross the Sefinnenfurgge, instead of going straight to Griesalp you can hike to the Gspaltenhornhütte first. Again, I haven't stayed there ( I got snowed out and had to drop down to the valley), but it is very popular and you would definitely have to book a place. You can start in Mürren and skip the Rotstock, but it makes for a longer day. I saw a recomendation recently that said it was advisable to cross the Sefinnen from east to west, but I did it the other way with no problems.
These hikes are all of a higher grade of difficulty than the day trippers do. There is an appreciable increase in risk and you have to be sure footed on some of the tracks. Don't expect safety rails - the best you will get are cables bolted to the rockface on the most exposed sections. All these ideas are completely weather dependent. The trails are well sign posted with way markers painted on rocks on the higher stretches, but in any case I suggest you take a map and compass as well as a pocket altimeter which is more useful if the weather closes in.
Have a look at the hut websites;