OK. In response to Adam's last post I will make a few suggestions to get the ball rolling.

Firstly, the 'correct' fix would be to remove the neck and adjust the heel and therefore the height and angle.
However, this would risk a lot of damage to the existing finish and also require an additional piece of wood under the fretboard/body join - not a good idea.

I would suggest removing the pu's and worry about them later.
Recess the bridge turrets into the body or source a much thinner bridge. It will need to recess such that the thumb wheels are flush with the body surface at least.
This will also introduce another problem though. The break angle to the end stop will now be too shallow so this will need lowering or replacing as well.
There is plenty of body depth available and flush or sub-surface turrets could look cool if done carefully.

Once this is done, check the action with a string. If happy then start on the pu's.
The bridge pu ring could be replaced with a neck ring - it looks like it would be about the right height. Maybe a little sanding on the bottom of it to get the profile right.

Turn the neck pu ring round and check with the pu screwed all the way out (down). Sand the ring until it is below the fretboard. If it looks like it will not work this way then recess the ring into the body by carefully cutting around the ring with a sharp scalpel and then slowly removing material and retry until the string still clears the pu when fretted at the 22nd fret.

Just a tip. If you do cut through the finish on the body, reseal the edge of the finish with cyano/epoxy/lacquer to avoid the possibility of the surface finish delaminating.

I know there are more steps to this and others may have better ideas.

Cheers
Ricky