Thanks, that was the very piece of information needed!
The body looks pretty thick. As @curtisa said you could remove material from the back without any changes to the setup. Based on the neck which looks factory made that's basically a Strat. A Strat body is 1 3/4" (45mm) thick with a deep belly carve and big forearm bevel to make it comfortable. You can easily go down to 1½", just make sure you leave enough space for the pickup, Floyd and controls. Some 1" should be plenty for the heel area, just make sure that the screws aren't too long. A belly carve alone could help a lot!