My daughter suggested peroxide - I might try that on something else I'm thinking about...
Ach, the more I look at it, the more I see it as a war wound, a reminder of a previous life, and I think that's a good thing.
A small update - moving up the grades, it's now sanded all over at 180 grit and starting to feel smooth. Also the 4 way switch arrived, and of course it's different to the original ones. A bit of detective work with a multimeter to check how the switch worked (it was pretty obvious really), a translation table was created then I rejigged the switch part of the schematic to suit this new switch.
Position 1: A -> 1, B -> 5, C -> 9
Position 2: A -> 2, B -> 6, C -> 10
Position 3: A -> 3, B -> 7, C -> 11
Position 4: A -> 4, B -> 8, C -> 12
A is wired to ground, B takes the (reversed) hot of the bridge pickup, C is final output to the volume pot. X means no connection.
Position 1 should give both in series
Position 2 should be bridge pickup only
Position 3 should be both in parallel
Position 4 should be neck only.