rdupilgrim,
During happy, easier past years late autumn and winter were the best times to walk the CF for me.
Accommodation started to close mid October but some place was always open. Hospitaleros usually could give advice on who/what was available on the next stage. There were no crowds and beds/bunks were available. I usually slept in an albergue, often the sole pilgrim, but also in back rooms of an open bar/restaurant.
Walking off-season during those past years I rarely saw more than 20 pilgrims at one time. There usually was a strong sense of camaraderie amongst those on the route especially during storms or difficult stretches.
Helpful passing strangers also gave advice. Little was hectic; without the hordes of summer all had time to share info.
Enjoy your planning and whenever/wherever you do go Buen camino.