Hi Hillary,
It will be busier around May 1st, but it won't be as bad walking nearer to Le Puy as it would be if you were leaving SJPP, (where it sounds like chaos ensues for a few days!) Since May 1st is a Friday, the whole weekend will in fact become a long weekend in France. Friday and Saturday nights will be the busiest nights to get a place, but Thursday and Sunday may also be busier than usual. Once you have been walking for a few days, by about the 26th, you will have a fairly good idea of the kind of pace you are making, and should be able to 'guesstimate' where you will be for the days of the long weekend. That would be soon enough to ring ahead and reserve. You might also want to think about getting demi-pension if you can around that time, as food can otherwise be tricky to obtain in France during long weekends.
You also need to watch out for booking on the weekend near May 8th, as well as Ascension and Pentecost whenever they fall this year. The French love their holidays and May has a few of them!!
All the best- it won't be long before you hit the trail! This time last year I was nearly in Paris, just about to head to Le Puy, and I find the memory of it all most exciting!
Margaret