Google is amazing. I searched for "underwater cobwebs" and my results turned up vermetid snails! I have never heard of them, but apparently they are a thing in saltwater/reef tanks. I don't know how they could be living in the dry, black lava rock I bought for my tank, but the webs they make look just like the ones I see!
Apparently the snails are sort of like embedded tube worms, lots of different kinds, come in different sizes, and use the mucus "webs" to gather food. Usually their tubes stick up a bit from the rock or coral or whatever. Funny thing is I don't see any tubes, and I don't know how they would have gotten into my tank. But the webs look the same!
This guy has them in his reef tank:
And here are some big ones embedded in a coral in the wild:
So maybe this is the answer!
