Peter,
It may seem like a dumb question, but how do you go about finding Moslem hotels?

Its a good question. Some are called something like, say. qingzhen dajiudian or yisilan binguan etc. - I cant recall the exact wordings right now, but the names got some hints. Same as moslem restaurants do.

Probably some tool out there that has more comprehensive info on this. Maybe a guide for moslem travellers in China or something like that. Obviously these hotels are more common over to north west.

These hotels can be great when you want to be on more sure side to get a normal sleep.

Nice info.