HHmm, as much as I enjoy all of the Le Puy route - depending on how much you need to skip, I think I'd agree with
@Murk that Condom to Arthez is a reasonable candidate.
I would not miss Lectoure (and not just because I live here) - it's a lovely town.
Buses
There is a bus a few times a day between Condom and Nogaro (bus 952) - if that's sufficient 'skipping' - it's about 50kms. And from Nogaro there is a bus to Aire sur L'Adour (bus 934) - a further 27 kms. But if the bus time don't line up, you'd probably waste a day travelling.
Passenger transport
La Malle Postale is a great service, but they only run between Le Puy en Velay and Lectoure. You may be able to arrange passenger transport say from Lectoure back to Moissac and take the train option as mentioned by
@Murk Here is the link. They are usually prompt in responding.
Transport of luggage and people on many hiking trails
Transport Claudine provides services from Lectoure to SJPP, Here is a link to their website. It says they provide a shuttle back from SJPP or Roncesvalles, but perhaps you may be able to arrange passenger transport between Point A and Point B with the baggage delivery van. Again, worth an email?
Transports Claudine-Compostelle-Vallée du Celé-Transports de bagages et personnes-Transfert véhicules-
I have a feeling there may be another provider now. I've seen the vans in town here, but I don't recall the name of the company. Maybe someone who has used it will see the thread? Or ...
And, perhaps,
@BlackRocker57 will chime in here. She is very knowledgeable on all things relating to the Le Puy Route. And she was on the Le Puy Way again, just a few months ago, so her information is recent.
Hope it all works out. It's a beautiful path.