In Olveiroa, since you prefer private places, I would highly recommend As Pias. It is the local place “de siempre” (pre-camino burst). It is a pensión and also the best bar/restaurante in Olveiroa. Lots of pilgrims there, of course, but lots of locals too. It’s charming — old stone building, white lace curtains. Maybe not as efficient or modern as the other places in town, so it depends on what you want. Whether you stay there or not, I would eat there - I’ve had some pretty bad meals in Olveiroa with a lot of menús del peregrino.
I know you said you wanted to stay in private places, but I think the Xunta albergue in Dumbría might be the exception. I’ve attached a picture It’s a modern, huge building, funded by the galego who started the Zara empire. Very nice facility with lots of common space and rooms with two bunks.
I’m not sure how to fit this into a four day walk into Muxia, but there is a
monastery/hotel in Moraime right next to a romanesque church with some very nice capitals and doorways. It’s very close to Muxia, though.
Buen camino, Laurie