This whole idea is interesting.Paint the magnets
to match the stonework.
1) If I start epoxying anything to stonework, someone is going to start having a hissy fit. The attachment is going to have to be into the mortar.
2) I have some 3mm dia neodymium magnets that I had toyed with using - but, as the mortar joints are recessed from the face of the uneven stonework, it would not be possible to get them to stick out far enough to engage with another magnet on the back of the board (reminder: these are foam board panels. They weigh in at under 150g).
3) It might be possible to use them in some locations, but, if they are so neat and invisible as they could possibly be made, once they are detached, few people would be able to put them back up again as they would never find the right spot!!
I suspect that this is a case where, the more high-tech you go, the more collateral problems you introduce. I can make sure that the small nail heads are placed where they are unlikely (I'm the H&S guy - I'll never say "never"!) to cause a problem. The "technology" is plain and obvious to any cleaner or visitor who detaches one and there's little to go wrong mechanically. These boards have to appear just to "be there" with no visible means of support and that achieves it.