So after weeks of pulling slimy grey flakes out of the drain filter every couple of loads, I decided to actually deal with it instead of just cleaning the filter again. Ran a hot cycle with a washing machine cleaner tablet, then a second hot cycle with nothing but a good scoop of the cheap powdered detergent. Figured the liquid stuff we'd been using for years was barely rinsing out and just building up in there. Third cycle in, the amount of gunk dropped off a cliff. Instead of a handful of that rubbery grey sludge every time, I got a light dusty film. Fourth cycle was basicly clean. I've done two more since and the filter is staying clear, so I'm calling it fixed. My guess is it was years of detergent residue mixed with lint that eventually clumped up behind the drum and under the door boot. It kept shedding into the filter because the whole lump was slowly breaking apart. If yours keeps regenerating the same grey mess, don't assume something inside the machine is disintegrating. There's a decent chance it's just old gunk letting go.
Might not work for everyone but it cost me about an afternoon and one cleaner tablet, way better than replacing a washer that had nothing mechanically wrong with it.