Please, no more major surgery. Do not let the perfect be the enemy of the good. You do not need a press fit between the neck and the sides of the neck pocket. The actual correction you need is tiny. There are thousands of teles out there with a little clearance on the sides of the neck, and they all sound good.Try this:
loosen the necks screws a bit
bump the headstock a little with the heel of your hand one way or the other (in this case it looks like ya wanna hit the tuner side)
tighten it up
If the pocket is too tight for Jupiter’s solution, relieve the sides of the pocket. 1/64” will probably do it. Use sandpaper on a very square block. While you are at it, make sure the screw holes in the body have some clearance for the screws. 11/64” is the correct hole size to allow the lateral play you need, and also allows the screws to draw the neck down tight in the pocket without binding.
Once you have these things done, final assembly using Jupiter’s method of adjustment is trivially simple and all you need.