I have no idea what I am talking about, but what if you used some shims and raised the neck up from the body a tiny bit. I don't mean to angle the neck, just straight up a tiny bit like a bank card thickness.
I would have thought that it would drop the strings closer to the frets, it's easier to remove the shims if it doesn't work then trying to build up the bridge if you mess that up.
But like I said, I am clueless as far as this stuff is concerned, I have only ever built one mini Les Paul for myself.
Love the work you have done, its been a great learning experience for you and me as well.
Cheers
Mick