I don't have an answer, but I wanted to say welcome to the forum and congratulations on your 5er.
I am more familiar with valves that won't open than I am with valves that won't close. I wonder if something solid has gotten into the valve and jammed? It won't be pleasant, but I would consider taking the stinky slinky off and pushing a rod up to see if you can push an obstruction back out of the valve. If that doesn't work, I would replace the valve. It is an easy job and the valves are not expensive.
Also, I would get that fixed. While an open gray tank valve doesn't lead to problems, an open black tank valve leads to the dreaded poop pyramid.
I live in the Memphis area. If I can help, I will be glad to try.