You’ll have upper bunks in pretty much all the albergues with only one rail - but I really don’t think that that’s going to be an issue for you. As
@David Tallan said, the chances are small if you actually needing to take an upper bunk. In the unlikely case that you do, ask to swap. I’m sure that people will be more than willing to accommodate you!
If that doesn’t work for you than maybe try this:
- La Robla - sorted
- Buiza - unpopular stop, very unlikely that the albergue/bottom bunks will be full
- Poladura de la Tercia - not much you can do about this. There are 6 bottom bunks, and I think some of the upper ones have double railings. Ask to swap if need be
- Llanos de Someron - private albergue, book a lower bunk
- Benduenos - all individual beds anyway (minus one single upper bunk). Let Sandra know and she’ll make sure you will be fine
- Mieres (individual room at university residence) or El Rollu (all individual beds)
- Oviedo - private room
So the crunch point will be Poladura de la Tercia. But again, I don’t think that the albergue will be full.
I’d be careful with the 30km days - the mountain days in the middle are though and you said you are slow on the descents. If you follow the suggestions above you have one longish day between Poladura and Llamos. Follow the Enders guide for the way that bypasses Parajes. The day will be long but doable and there will be fantastic food in Llamos waiting for you.