John, more knowledgeable people than I will surely respond, but from my research (September this year, God willing), here's what you might see...
The entirety of Santa Semana (Holy Week) could be dicey, as some places may simply close, especially during Holy Thursday through Easter). Easter Monday isn't such a big thing in Spain, AFAIK (as far as i know). On the other hand, the festivities and parades are said to be wonderful.
Also, there are some early stages on the Primitivo where there aren't services for a long way. So everyone tends to load into the same places.
To add to this, again AFAIK, you can reserve in private hotels/hostels, but not in municipal albergues and perhaps some donativos.
My suggestion is to download either Buen Camino or
Wise Pilgrim, and look at your options, and consider guessing and prebooking Good Friday thru Easter. And call to make sure they're open.
Buen Camino.