Hi, JAO, and welcome to the forum....
I noticed that lodging, in general, in SJPdP was becoming more difficult to locate as I was looking at reservations for September 17 this year.... and that was back in February.
St Jean is popular with both tourists and pilgrims during the fall season, which is why I had started looking at the lodging situation so early; I wanted to get a feel of how things were going. I remember posting about this back then as someone had talked about whether or not to book a room for early September, even though it we were just barely into 2018.
You can reserve a bed at the albergue in Roncesvalles.
http://www.alberguederoncesvalles.com/reservas.php
There are also lodgings in Burgette and Espinal, which are about 3 and 7 km further along from Roncesvalles, although Burgette, especially, is also popular; but fewer pilgrims plan on spending a night there. At any point along Camino that lodgings are fully booked at your planned daily stop, you can always take a taxi to the next town and then return to your stopping point the next morning, if you find yourself too tired to continue.
So, for example, if you get to Roncesvalles and the albergue is completo, then take a taxi (if the extra 3 km is too much for the day) to Burgette or Espinal, spend the night there, then taxi back to Roncesvalles the next morning.