Endless empty hot cycles to flush out sediment, or is there a smarter way?

My issue with a Whirlpool front loader was similar, but the buildup was more of a hard water mineral scale issue rather than just sludge. After running cycles with Epsom salts and vinegar for a week, the gunk kept appearing, so I figured the internal lines were completely coated. Flushing wasn't going to work. I decided the only way to gaurantee a fix was to pull the supply hose off the back, and then run a specialized descaler through the washer itself. It took two hours of careful unscrewing and scrubbing with a stiff brush, but it made a massive difference. I think you are probably past the point where simple cycles will ever fix it. When you see bits dropping out of the drain hose, that means the clog is extensive and likely involves the drum seals and the inlet valves, not just the pump. If you haven't already, look into a full tub disassembly. At least for the exterior parts, you need to access the interior baffles and manually scrape off what is there.

Don't just focus on the main filter. The tiny holes in the wash inlet are notorious for holding debris. A proper manual scrub of those connections is usually what stops the constant shedding. It is messy, but sometimes you just have to get in there and wipe everything down until it is dry.

I had a lot of trouble with the same gray powder coming out of my Kenmore washer, and honestly, I think the issue was not deep inside the drain lines, but rather right at the top where the water enters. The gunk was so fine it looked like dust, and no amount of washing soda fixed it for me. After a few weeks of frustration, I realized the minerals were prolly coating the intake valve or the small mesh filter just before the water enters the drum. You can't really clean that from the front panel. I grabbed a small brush, the kind you use for cleaning grout, and some white vinegar, and carefully disassembled the water inlet hoses at the back, just enough to get the housing open. I used the toothbrush to scrape the sediment off the actual entry points. It was surprisingly dense, almost like fine clay, and a huge amount came out when I rinsed it. The next few loads were completly clean, and the problem didn't come back for over a year. Since the previous reply suggested tackling the internal lines, you might consider that route. But if you want a cheaper first attempt before a full teardown, check those intake screens first. It was a major surprise because it wasn't obvious where the blockage was happening.

Agree with the poster who said to look at the intake side. Mine was doing the exact same thing for months and it turned out the little mesh screen inside the water valve was half full of rusty sediment from our old street pipes. Every fill was dosing the load with fresh grit. I pulled the screen out, rinsed it under the faucet with an old toothbrush, and the flakes stopped within two loads. Check that screen before you tear the whole tub apart, it's a ten minute job.

Before you start pulling anything apart, check how much detergent you're using. I do appliance repair on the side, maybe a dozen washers a year, and this exact gray sludge is almost always overdosing. The soap can't rinse out, it mixes with soil and body oils, and it sets like rubber in the drum and sump. I had one customer using nearly a full cap per load and it took me four test washes with a single tablespoon to flush it all through. If your detergent is HE and you're seeing suds mid-cycle, that's your culprit. Try cutting the dose way down and running a few washes with towels you don't care about.

First post here so hope this helps. Mine turned out to be old towels falling apart. The lint was getting stuck in the sump under the drum and every wash spat a bit back out, so it felt endless even though nothing inside was dirty. One thing I did that gave me a clue was dropping some of the gunk in a glass of water and leaving it overnight. Soap residue kind of dissolves and clouds up, mine just sat there as fibres. That's how I knew it was coming off the laundry itself. Might be worth a try before you start unscrewing anything, it's free at least.

Update: pulled the mesh screen out of the water inlet valve and it was packed with rusty crud, so that was half my problem right there. Cleaned it and the grit coming off on clothes has way down. But there's still some waxy gray film inside the drum, so maybe the repair guy is right about me using too much soap. How do you tell how much is acutally too much for a front loader?