Interesting... When it comes to pilgrims from outside of Spain, the spikes are in May and September (from my experience here in Santiago). It it all the pilgrims from Spain that makes the spike happen in the middle of the summer.
I was thinking of going in January, mainly because I keep putting it off due to work. Would this be a really bad time and would the hostels be open? It looks from is graph as if no one goes this time of year?!
Some of the experts here will likely provide more insight but from what I've read there are always places to stay, but in the "off months" there are fewer of them. You may have weather issues at the higher altitudes of course. The Napoleon from SJPdP will certainly be closed for example. But you'll have the Camino to your self practically.
My OCD side has gotten the better of me. The horizontal scale on this graph is slightly wonky. The months on the scale don't match the data points on the graph and there are random missing months on the scale (Feb, Apr, Jul, Sep) combined with an extra Jan. There are twelve data points on each of the graphs. Expect you could label the data points from left to right - Jan to Dec and get a slightly more correct interpretation.