Galley gray tank, not main gray tank. The shower won't be involved.
OP, I am afraid you will have to push a plumber's snake up the drain. That will be messy.
I, also, had a plug from a cut-out. Mine was in the black tank where they cut the circle on the top of the tank for the toilet drain. I didn't know what the problem was until I had owned the RV for about 3 years. I was at home draining the tanks with my Flojet Macerator and using a clear section so I could watch for clear water flow. I saw the circular piece of plastic fall into the clear section. No problems since that came out.