I think I have got to the bottom of it:
My Drawing Template was calling up the latest version of the .sldstd file, but the part template was calling up an earlier version, in which the diameter dimensions had been set to the crazy font.
I have noticed before (but clearly not the last and most important time) that fonts are changed to the crazy font when I make some other change on the same page of the .sldstd file. I don't know whether that is a bug, or simply my incompetence.
Whichever, the problem seems to solved for the moment.