I like the idea of the natural cut stone. I haven't seen it done recently, but there was a guy I knew years ago that could cut stone using a circular blade on a modified wet saw. Very similar to cutting ceramic tile, he would make cuts into the stones but not all the way through then he would chisel tap the center out.
If you need a tunnel type hole you can use a wet saw and a hole cutter bit and work it through the rock, they do they for cutting holes in counter tops for bath and kitchens, I have gone in and picked up the holes left behind as scrap before and watched them work.