I'm assuming you are talking about the fuel feed pump at the rear of the car, near the fuel tank and not the fuel injection pump, right?
"Frozen again" means its been frozen before; did you ever install a rebuilt pump, or have yours rebuilt? Sounds like an issue with your pump at the end of its service life, meaning something has failed. Check with Bob Youngman (baronyoungman) as he is our resident expert on pumps having rebuilt many.
There's always that possibility that the gray gunk is some jelled fuel mixed with metal particles from something wearing excessively. I think the impeller is hardened aluminum.
Its possible you've got some water in your fuel system and on a car that doesn't get used often this can be trouble. The fuel stabilizer (Lucas and others) are pure petroleum products not likely to cause harm.