Jenny. I don’t think you need to second guess your original plan to start on the Frances. At least not yet. You must have chosen it for a reason or more than one.
If you find it too difficult with accommodation you can always switch to the Norte, though there’s no guarantee it will be easier. There are various points on the Frances where you can take a bus to Irun or San Sebastian or Bilbao, for example. With 40 days you likely have some time up your sleeve to be flexible.
As to accommodation concerns in September leaving from SJPP you’ll find many suggestions on the forum for booking as far as Pamplona after which ‘crowds’ tend to dissipate. That might give you comfort for those first days.
You’ll also see many posts about accommodation on booking sites being hard to find at certain times, while calling properties directly can be more successful. Not to mention non reservable Albergues that some people report having plenty of spare beds even amid a big ‘wave’ of pilgrims.
I don’t in any way dismiss the reports of ‘busyness’ that are concerning you. But I think the Frances offers more accommodation and flexibility with stages too, eg stopping a few kms short of where you may have anticipated or walking a few kms further.
In your shoes I’d stick with your original plan, be ready to adapt IF needed inc switching to the Norte. But I wouldn’t be surprised if it doesn’t come to that.
Whatever you decide, all the best.