Hi all
Many thanks for the assistance. I've tried replacing the potentiometer with resistors in series, and the hum arrives as soon as the resistors are in the circuit - so perhaps it's not the pot.
I ordered 75k Ohm resistors, but their colour coding is Brown, Red, Black, Green, and a thin brown. I think that makes them 2MOhm, if I'm reading it right, at 1% tolerance, but at any rate, I'm not sure that they really are 75k Ohms, although my multimeter seems to think they are (assuming I'm reading that right, as well ;-)
So my next step, I think, will be to move to a 110k pot with a 25k (or 15k) resistor for log taper. If that still introduces the hum, I'll try for the full circuit so kindly suggested by sashijoseph. If that still doesn't work, I'll post again. But since I'll have to buy the parts, it'll only happen in the new year.
Many thanks to all, and a merry Christmas season,
All the best,
Craig