I sanded the neck down so it would go in tightly and did a mock build.
There's a couple of minor issues which shouldn't be too much of a problem:
The routing in the control panel is not quite deep enough, so there isn't quite enough thread on the pickup selector switch and output jack to fit all the washers
One of the tone knobs doesn't push down fully so it sits up a bit (I'll probably get some different knobs anyway)
When I had the neck lined up with the pickup route I got the following measurements:
Adjusted back
Adjusted forwards
Low E
321mm
315mm
High E
318mm
313mm
I get 313mm for the nut to 12th fret, so I think it should be ok as is?
I've added some photos of the neck - there's about 1mm difference in the distance from the last fret to the end of the fretboard on either side. So there's a slight gap when the cover is in place. I think it will be fine, I'll just make sure to blacken that bit of the neck so it can't be seen.