Recently I got a handrouter; so as a test I also routed out a cavity of 1 cm from the back and front panels. Here they are, finished routing:
Then I glued the three parts together. I used standad white wood glue from the DIY store, 6 clamps (maybe it's not enough, but we'll see) and a weight to push it together.
A day later, I sawed the body with a jigsaw. It is clear a bandsaw and router would give a much straighter result, but I don' have a bandsaw, and no tracing bit on the router... and was interested how things would turn out like this.
So this is how it looked, with pickguard, bridge and controlplate for reference:
Then I routed out the neckpocket... and made the newbie mistake to not measure thrice but only twice... :-) It was routed 3 cm while it should have been only 1.5 cm. So I glued a piece of wood in the neckpocket and routed it to the correct height.
That doesn't look pretty, but I guess it will work.