Since caves will likely be connected cardinally instead of being stacked on top of each other, I figured it leaves me an opportunity to play around with the Z-axis. Release the heightmaps!
Aaaand the cross-section.
Coming from the right lets you climb down safely, but changing the layer takes an extra turn. If you came from the left, you'd get hurt by the high fall, plus you couldn't climb back up that way.
For gameplay reasons, I think it would be fitting that you'd only see the very edges of the layer above. In that pic, the player would see the light grey, dark grey and black areas completely, but the highest layer would be out of sight, apart from monsters staring at him from the ledge tiles. This encourages you to stay on higher ground whenever possible. You can't walk into the black void, but it differs from a wall in the sense that you can see through and toss stuff over it.
There's still a bit too much noise for my liking, so I'll have to tune the generator a bit. Obviously I'd prefer uniform areas if they're going to behave like layers. Particularly large chasms (which I'd like to see) look too pizza-like with the current cutoff: