I have been in Cordoba and Caceres during festival events, and yes, accommodation was a problem, even in the neighbouring towns. I think it is great to be on the Camino during Easter week and during festivals, but I would do it with some awareness of the fact that many Spaniards travel within their own country.
If it were me, I would make my best guess for arrival date in Santiago during Easter week, and I would book a place on booking.com that can be cancelled up to a day or 2 before arrival. There is no harm in booking that now, for the Good Friday-Easter weekend. Then as the time gets close, you can always cancel if your plans change, being aware that alternatives may or may not be plentiful. If you are going too fast and approaching Santiago too early, then slow down!
I don't know the Camino Portuguese, so I can't speak about the accommodations along the route.