Succulents don't like their feet wet so maybe consider a semi-water plant?
But if there's a dry spot, maybe small succulent can survive...?

What about a miniature fern?

When I was a kid I made these little gardens in seashells and kept them in my room. Most of the plants were actually weeds I found around outside (a weed is just a plant in the wrong place!). Anyhoo, I was thinking that maybe something suitable could be found growing in a wettish area; something that doesn't grow too big. My 2 cents.

Great idea Connie.

Thanks for all the ideas.

I gave it some thought. In addition to surviving in very wet soil, I need to find a plant that can grow in poor soil (due to constant exposure to the hard water in the waterfall). And I also need something whose roots are shallow and noninvasive (won't burrow into or through lava rock).

I don't know much about the root system of ferns, can they survive with shallow roots and will they burrow?
For that matter, will semp roots burrow into lava rock?

Semps won't survive all that moisture. There are some sedum that will cling to porous rock.

Also I think semp roots can get quite long, so possible that it would burrow! I mini fern would probably have less of a root system to worry about

Yeah, I wouldn't try putting the semps in the wet right spot.
There's a cleft/shelf on the left side that is dry that I've never attempted to plant anything there, but since I've gotten into semps it seems like a perfect spot for a small clump. (If they wouldn't cleave the rock off eventually due to root growth, of course.)

Ah okay, thanks Greg.

Is this water fall rock staying indoors? Because semps would be challenged by that, but there are several echevarias that look very similar to semps and would probably fit the bill if indoors!!

Yeah, it's inside but near a window and also near a lamp that is nearly always on. I wouldn't expect any color change from green or anything, but I will also look into echevarias. Thanks again.

JC in my experience trying to grow them indoors, these guys seem to like a lot of airflow, and I didn't use a fan or anything, they stayed small and green like you say, but almost dying, and then as soon as I planted them outdoors they took off!!!

Okay, I'll wait to try that experiment until I have more chicks than I know what to do with, then maybe give it a shot with just one little one.

haha yes!! In my imagining I say that semps don't do as well indoors because they're usually up where the mountain goats roam...but so many are hybridized in gardens at sea level, so I'm not really sure what is "true"
I fully admit I have a very active imagination!