I have researched the most affordable and generally best sounding accommodation according to the internet. There is a list for each place, sorted roughly from most desired downwards, they are in each day of the trip.
Basic process for finding accommodation:
https://www.activityworkshop.net/hiking/alpinepassroute/index.html
http://www.via-alpina.org/en/stage/109
https://myviaalpina.wordpress.com/
https://longdistancetrail.wordpress.com/trails/alpine-pass-route/
https://www.cicerone-extra.com/switzerlands-alpine-pass-route
The phone numbers below are good to have at hand when traveling in Switzerland.