I have a similar issue with RA.
I think there might be some kind of classifying system in place of patients as I'm always asked which card I am when I make an appointment. Maybe to prioritise patients with conditions like diabetes.
I must admit though I've never had to wait very long for an appointment, they were very quick when I had ingrowing and involuted toenails and for the surgery for that (though they did keep getting infected and I have a duff immune system).
I don't go very often for toenail cutting but it's never been more than a week or so wait. Due to the RA it's forcing some other toenails to grow not straight and causing problems.
I managed to find some longer handled toenail cutters. Podiatry also recommended trying to keep them down with a long emery board in the meantime.