I don't have any experience on the Eastern side of the Himalaya, but I did some travelling on the Western side in China, in areas with high numbers of Tibetan people.
As usually I did not plan or book anything but mostly stayed in hotels in towns, but a few times I also just walked in the mountains through some villages and when I asked people for a place to sleep, they more often than not offered me a room in their house. Some times I just stayed one night, but in a few cases also for a few days, but never for a month.
In most cases nobody in the house spoke any English, and I didn't even know what language they spoke, usually not Mandarin. So regardless the problems with communication, I had a great time with the families, I will always remember the meals with a big family in a huge beautiful Tibetan kitchen.
It was super cheap too, a quarter of what I would pay for a room in a cheap hotel in the next town and the food was included as well.
I sometimes feel that the 'families' that offer home-stays through commercial agencies are in there for the money and they are very used to having foreigners in their house. It's a business for them. The people I stayed with were super interested in me, it's a shame we couldn't talk to each other, but even just showing photos or maps was fun. And you can explain a lot with your hands.
Your hosts may also know other people in the next village and can hook you up with someone where you could stay a bit longer.
If you 'book' ahead and then you don't like the place, you still may stay just because you already paid for it.
I'm sure this way of travelling is not for everybody, but it is an option in many rural areas.