Well, having now got around to putting a meter across the battery contacts
(at the PCB end of things) while a battery was fitted, I find that no volts
were getting through. Which, as far as it goes, is a nice easy solution and
a slap on the wrist for me for not doing this earlier.

Jamming a bit of foil between the +battery contact and the battery itself
makes the clock tick with any battery.

But I'm still puzzled, because

-All the batteries I've tried are a nice snug fit, so contact should be good
anyway
-I've cleaned and recleaned the contacts with emery paper even though there
was no visible sign of corrosion.
-The design of the battery contact, while not perfect, ought to be making
good electrical contact with any of the batteries I've tried. It's
certainly pressing against the battery
-The original battery always worked when put back in, even though it's
contact profile is near-on identical to the other brands of battery I tried
in the clock

Bizarre, but I suppose that's the way with battery contacts.

Still, at least it shows the module is working. I'll probably blob some
solder on the battery contact if I can't work out any other way of improving
it's (already seemingly good) physical contact with the battery.

Thanks for all your suggestions though!

Ian