Probably too late to the party, but are there any internal soil pipes, as the boxing in of them, might be an ideal route for cable?
You might also have some cupboards that you can take up the flooring of, and push PoE AP’s (like your Unifi) towards the centre of each floor, between the floor joists? In your situation, I’d guess that going through floors is a hell of a lot easier than those walls. If needs be though, it’s generally not difficult to use an SDS Drill like this:
and a drill bit like this
Steering away from going through stone, you should have eaves front and back and these can be used to feed cables down the wall and through what I’d hope would be timber windows? (Someone did mention this already) You’d have to crawl in the roof space around the smallest area though, so flexibility is needed! 
It wouldn’t look very nice though, having cables down the outside, and you’d need external CAT cable…mind you, I had basic cat cable going to my shed for a year and it worked fine.
A weird edge case is if you had a chimney stack that was unused, that would be an easy place to drop cables?
Hope that helps a bit.