Seems like a classic shim job is needed....

I'd be cutting a 1cm wide strip of plastic from a 2L icecream container lid as long as the neck is wide, and insert that under the very end of the neck between the neck and the body... reassemble and check your string heights again and see where you are at. It is as close as a home builder can get to what many manufacturers and luthiers do to correct similar issues.... You may even need two such shim strips.