Well tonight I did a little playing with a Dremel in a router table and cut down the scratchplate based on my paper template.
It's not quite there yet and I've yet to start on the pickup cutouts but it's looking believable rather than a ridiculous wobbly mess.
I've cut the neck pocket too large and it still needs a fair bit trimmed from the lower edge but I'll work on that carefully. I've got a few days off over Easter so I'll have time to tackle this.
If I mess it up I'll just buy another piece of scratchplate material, it's not massively expensive for simple 3-ply. I was thinking of starting with a piece of clear perspex to make a template but abandoned the idea as I'd just end up doing the same work twice.