Speed Queen TC5 is what you want. It's their Classic washer, functionally the same as the ones they've made for decades. Agitator. Transmission. Manual dials. All the same as the good old days.

It only has one "super efficient" cycle, the Normal cycle, in order to meet mandatory government water usage standards. (Which are apparently calculated as an average across all cycles, so having one super low usage cycle helps counterbalance all the moderate-to-high water usage cycles by skewing the overall average water usage down dramatically.)

All the other cycles are non-HE. And there's even a further option for a full tub fill. In practice, you just rarely ever use Normal unless you only have a very small and very lightly used load, and use the Permanent Press cycle as the standard cycle. That's actually the advice of Speed Queen Customer Service.

The Normal cycle is super fast, though. So it could be handy for times when you just need to wash one or two outfits.

Last time I bought a washing machine, the HE designation was new to me and sounded like something I did not want and I thought I bought a non HE machine, but I ended up with one. At least once a month, the clothes come out smelling foul and I have to run a cycle with some soap and a lot of bleach to get rid of the smell. Never dealt with anything like that before. Never heard of Speed Queen before and I see that they are very expensive, but no more damn HE washing machines for me. Nope!

We have the Maytag commercial model Skins and others have suggested in our apartment and are really happy with it. It uses a pantload of water and actually gets the dirt and soap residue rinsed out of the clothes, unlike any of the piece of crap HE frontloaders we’ve had for the last 20 years.

I’ve successfully washed a king size comforter in it many times as well.