Well, as usual, I got the itch with regard to the magnetic handles idea, so I had to put one together…
First, I milled (planed, actually) a stick of 1" X 1" ABS down to 0.935" thick, figuring that the stones are an average of 0.125" thick. The target for from face to face distance is 1.187". 1.187" minus 0.25".
I machined four 1/2" diameter by 0.125" deep pockets to hold the neodymium magnets I had on hand. On the first side, I used a router table, as it has a relatively accurate vertical adjustment. Unfortunately, the lowest speed of my router was still too fast for ABS and the plastic melted in the center of the bore, even though I had pre-drilled it to 1/4" diameter.
The opposite side of the handle was drilled with a 1/2" diameter Forstner bit. The ABS didn’t like that either and the holes were slightly over-sized, making some form of glue necessary, and the depth was harder to control, requiring a bit of shim stock to make them even.
The magnet had to be pressed in on the router side, and would probably need to be glued in on the Forstner side.
On both sides, the magnet faces protrude slightly from the handle, resulting in a slightly larger distance from the center of the guide rod bore. It did not, however, appear to make the stone faces unstable. They are solid and would not move around without some deliberate external force being applied.
You can easily slide the stones off to the side, or for that matter, to the end, when needed to change stones.
I added a screw-driver notch on each side. The photos below show that capability. Although this worked quite well, I think I’d prefer to push the stone off toward one end or the other. If you lift the stone away from the magnets, they’ll find out some way of pinching you to see if you scream like a girly.
In use, I don’t see any reason why the magnet-held stones wouldn’t work just fine. One simple change to address any concerns about stone position would be to add a very small raised section along the edges to keep the stone centered on the handle. Imagine the current handle design without the raised edges at the ends.
No, I don’t have this handle configured so that I could actually test it in use. Meanwhile, I be glad to answer any questions.
Here’s the first photo showing the handle without stones:

Next shows a stone attached, but turned to show the magnets and the notch for the screw-driver removal:

Next is the mounted stone, showing how a screwdriver could be used to lift the stone off of the magnet faces:

And last is showing how rotating the screwdriver (very little effort required) would break the magnetic hold, allowing the user to remove the stone:
