The challenge that presents is that you must have a 100% seal between the rock and the liner,or you are going to be losing water. I have tested construction adhesive, and I will probably take that approach. Perhaps with multiple, overlaping joints.
I fear you are going down a common DIY path of what I call gooping it up. Adding more and more thinking that will fix a leak. See it on roofs...a lot.
When you say "multiple, overlapping joints" I don't get a good feeling. Less is better. Multiple joints means multiple places for leaks. If it can't be sealed in one joint it sure can't in multiple.
Is the adhesive rated for use underwater? Not waterproof, but underwater. The reason most aren't is because they don't last underwater.
So say you use an epoxy that can stand up underwater. Super. Here's the problem, it's only as strong as the material it's bonded to. The rock will have a very strong bond...as long as the rock stays relatively dry. Once you run water over the rock all kinds of tiny critters will set up house. Over time they will grow and get in between the materials, weaken the bond and fail. Caulk around a bathtub is a good example.
This can also happen with the bond to the liner. And the bond to EPDM is not great to begin with.
There will be a line of weekend DIYers around the block to tell you this goop or that goop is just the perfect goop, the magic goop, and no one else knows what they're talking about. Welcome to the internet.
But then there is the manufacturer of the goop saying their goop should not be used underwater. And if a underwater use is allowed there is a long list of restrictions which will include structure use which your project is.
Then there are professional installers who would never use goop because their careers are on the line.
Then there is my absolute favorite...goop looks so darn easy. You buy a tube, squirt some on the rock and stick the liner to it. Wow, that's so easy! Then you start. Squirt a bead on the rock, stick the liner on and what, hold it with your hand until the goop sets up? Kind of hope it sticks? Adhesives require clamping pressure during setup. That is very hard to do on a vertical rock surface. You need a bunch of cross bracing or something.
On the other hand a thick neoprene gasket between the liner and rock, with a plastic board or aluminum flat bar on the outside of the liner and screwed into the rock will work for decades, is not much more expensive, and is actually easier. Also doesn't look like a mess.
And should this not pond idea work out? Removing goop from the rock....oh, that's fun. And like will scar the rock. Or unscrew and patch the holes with some matching sanded stucco caulk so the holes disappear and you are done.
Now I get virtually all people who post questions are actually just going to do whatever they're going to do. This post is more for readers got here from a Google search.