Lovely plant!

Do these have the typical soft fleshy succulent texture, or do they actually have a harder stone-like feel to them?

Not too soft, but as the leaves goes more mature the rocky looking surface will feel quite firm to one's touch.
The warmer and drier the ambience around it goes, with as much bright light access, the better it looks, more pronounced pebble-like appearance on the surface of the leaf.

Otherwise the rocky looking surface will not be too prominent.

file photo 16Mar2016

The leaf tips are firm but the leaves themselves are flexible (not stiff at all). So interesting.

They look tough but they're total softies. Pretty average for a succulent leaf, at least in that family.