Thanks for the advice, Tom. In fact, I was one step ahead of you.
I'd already stripped the module yesterday.
The PCB cleaned up quite nicely using ElectriCor VCI238 aerosol spray (akin to WD40), and gentle probing with cocktail sticks.
There's some minor collateral damage around the resistors near the battery contacts:
But as you correctly assumed, the -ve battery terminal was toast; it's imprint remained only as verdigris:
I don't have anything in the way of an LCD 'bits box', so as a first attempt I'm going to try to fabricate a new -ve terminal from an M4 solder tag.
This want ad is a 'back-up plan', in case my unqualified (LCD-wise) efforts fail.

Some watches are made to last only as long as they are fashionable.
Some watches simply aren't made to last.
Seiko watches are designed to withstand the ravages of both time and fashion.
Some day, perhaps, all watches will be made this way.