We're pretty blind here without pictures.

There haven't been any major issues like this on other JB builds that I know of. My gut feeling is that the bridge is slightly out of place and if you move that, then there should be some wriggle room in the neck pocket to align the neck so that the strings run correctly over the pickups with the scratchplate sitting happily around the neck pocket.

But without pictures it's hard to tell if that's anywhere near the reality of the situation or not.