I am now experimenting with different thickness picks, and as I can't get to a music shop right now using a pick punch to make them out of old credit cards (though the ease with which I was able to buy a new Fender last week suggests I might be better off using my current credit cards as picks!) and then gluing them them together. A single pick, as I have used for the last 2 or 3 weeks now, is about 0.7mm thick, so I stuck a couple together, and it felt better, then I added two 'top halves' to thinking the area I grip up to nearly 3mm, and it does feel better. I am now making one with three central laminations and a grip thickener on each side, which will be over 3.5mm, and I'll try them out at rehearsal tonight. That is, if I can unglue my fingers.
At least I will have some idea of what to look for next time I am able to get into town.