Unfortunately, the shellac experiments failed to reproduce the problem that I had with the polish that failed to harden. I put blobs of shellac from each of the containers of the stuff that I had in the workshop onto a sheet of glass and left them overnight: all hardened satisfactorily. So I can rule out the possibility that the shellac I was using was too old.
I also French polished a piece of scrap mahogany, using a lot of mineral oil on the rubber and building up a thickish layer as quickly as I could. That worked fine. So Bob Flexner was quite right when he said that it wasn’t the oil causing the problem.
I’m left without an explanation but I have learnt something. First, it’s always worthwhile to check that the shellac hardens using the ‘blob on glass’ technique before starting to polish an instrument. Second, mineral oil is an effective lubricant for the rubber and doesn’t compromise the quality of the finish. And third that, if the polish doesn’t harden fairly quickly, the best thing to do is wipe it off and start again rather than waiting around in the hope that it will harden eventually.