In late August 2019 I walked from Dax, a fascinating town founded by the Romans, with impressively hot natural thermal baths (there is a pilgrim Gite, not far from the railway station, though you have to give advanced warning to the local association, so a volunteer can meet you with the key). From there to Sorde l'Abbaye (another pilgrim facility, staffed by volunteers) is 25kms. Dinner is usually available, if you let them know you're coming. Sorde to Saint Palais (with its buoyant hostel, with single and double rooms) is a rolling 34kms, with an option of splitting the stage at Bergouey (there are accomodation options there but I'm not clear what). Finally, Saint Palais to Saint Jean PdP is 34km, with the option of dividing the stage at Ostabat (11kms), which has a range of accomodation options.
By the time I arrived in SJPdP, my legs felt fully warmed up and the climb up to the Col felt comparitively easy!
As other have said, Aire sur l'Adour is another start place option, if you can spare a few more days. You would have more fully catered Gite d'Etapes to enjoy on that last section of the Voie du Puy.
Enjoy! Bon Chemin!