Progress!
It might not look like much, but the body has been thicknessed to the correct depth, more or less by hand. I used the router to remove a lot of the "bulk", but that a lot of router marks instead. So out came the planer, which removed a lot of the router marks, and left planer marks in their place!
It would have taken all of 10 mins on a drum sander. Instead I got to use a sanding block, a load of 60 grit paper, and a lot of sweat. It's not near finished yet - I need to smooth the edges some more, and then work on the body with smoother paper - 120 then 180 then 240 grit I think. By the end of that lot, (a) I'll be knackered and (b) the body should be smooth enough to oil finish.
The bit where the neck will go is deliberately untouched - this will get cut off when I prepare the neck pocket. In the meantime, it's a handy place to fit the clamps!
I'm really happy with the colouring of the wood, and the grain that's getting exposed by the sanding. These photos don't really do justice to it ...