If anyone knows of one of those Maytags for sale, I'm interested, as a backup unit and for mechanical interests (geek factor

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You can still get new twinnies in the USA: Danby and Haier. This year I got a Danby DTT-420 which is excellent. I haven't seen the Haier first hand. I also have a conventional Hotpoint TL, which came with the apartment. Both machines are useful; the Danby does most of my laundry and the Hotpoint does large and/or heavy/bulky items.
Capacity: The Hotpoint TL is rated at 12#, but realistically holds 8 - 9 #. The Danby is rated at 10#, but realistically holds 5 - 6#. So, two loads in the Danby twin tub would be one load in the Hotpoint TL. (I can't see any way to design a compact washer to hold more than 5#.)
Cycle time: The Hotpoint TL takes about an hour to do 8 - 9 #. The Danby twin tub takes 1/2 hour to do 4-1/2 to 5 #. In effect, the time is the same for 9# of laundry (one load in the Hotpoint, or two in the Danby). The faster cycle of the Danby lets me wash smaller loads more often, which is convenient for me given my schedule.
Twin tub cycle: You can vary the wash/rinse and spin times to suit the conditions. What I've been doing lately is: Wash: 9 minutes; during the last 3 minutes I run water through the tub at about 1 gallon per minute, to provide a partial rinse that floats off the soap suds and soap scum and makes the actual rinse cycle go faster. Drain the washtub while transferring load to spinner (no lost time waiting for washtub to empty). Spin: 2 minutes, during which time I re-fill the wash tub with rinse water (also no lost time here). Rinse: 9 minute rinse in "overflow" mode with water at 1 gallon per minute. At the end of the rinse, the water in the tub is clean enough to save for the next wash. Transfer load to spinner, final spin 5 minutes. Done!
After hanging up the laundry on the line, I go back and add a teaspoon or two (approx.) of bleach to the rinse water in the washtub to keep it sanitary, and leave it there for the next load to be washed in a couple days. This effectively gets my water consumption down to about the level of a front-loader (and yesterday's rinse water is more than clean enough to use as tomorrow's wash water). When I finsh installing the graywater reclamation system, my overall water consumption will drop further: the used washwater will go through a lint-screen and into a holding tank to be used for flushing the toilet during the week.
Electric power consumption: I just measured this weekend using a clever KWH (kilowatt-hour) monitor which I'm using to check all my appliances' power consumption. Interestingly, the power consumption for each machine was half of what I had expected based on the rating plate on each machine. The Hotpoint TL uses only 0.26 KWH for 8 - 9 # of laundry. The Danby twin tub uses an amazingly small 0.06 (six one-hundredths!) of a KWH for 4 - 5 # of laundry: half as much energy consumption per pound.
I suspect the lower power consumption on the twin-tub is due to a) the agitation action, which runs the motor intermittently, and b) the spin cycle does not have to rotate a large heavy tub full of water while getting up to speed.
Agitation system: The Danby twin tub uses a conventional agitator, not a "pulsator" disc. Agitation is intermittent: "Gentle" mode: One second counterclockwise, one second pause, one second clockwise, one second pause, repeat until done. "Normal" mode: One-and-a-half seconds counterclockwise, one second pause, one second clockwise, one second pause, repeat until done. Yes, that extra half second counterclockwise in the "normal" mode does make for a darn vigorous washing action! And the gentle mode is gentle enough for most things, though I wouldn't go putting truly delicate items in any washer except possibly a modern FL.
"Indigestion" threshold: Only once have I managed to put something in the Danby that gave it trouble. This was a load that included a full-size flannel sheet and two large bath towels. The wash motor made a funny noise that sounded like a cogged belt slipping, so I immediately removed the towels at the first sign of that noise, and washed them after I was done washing the sheet. No further trouble has occurred. Also once I tried pouring water through the spin tub whilst spinning, this caused it to bog down and I quickly stopped that experiment. No trouble with the spin tub since then, using it as it was designed (see below).
Spin efficiency: This weekend I did a load in each machine, and after the Hotpoint was done with its load, I ran the same clothes through the Danby spinner. It spun out about another pint of water per each 4-1/2 # of laundry. So if you have "both" a conventional washer and a twinnie, you can shorten your drying times by using the twinnie's spinner after your conventional washer is done.
Sound levels: The Danby is quiet enough in all modes, that the loudest sound I hear is the water splashing into the washtub as it fills. When the spinner gets going it sounds like a quiet version of a jet engine winding up, which is kinda' cool. If you load the spinner off-balance, it will vibrate and you'll definitely hear that. If you hear the spinner vibrating heavily, open the lid to stop it and re-load it. This is a minor inconvenience and you'll pretty quickly get the hang of loading it so it's properly balanced.
Comparison of rinse methods:
From what I've read, standard practice with twinnies in the UK is to use a "spray/extract rinse" where water is run through the spin tub as it's spinning. The UK machines, notably the old Hoovermatic, were designed to spin at 3,000 rpm, which may have something to do with this.
The Danby isn't designed to do that. Spin speed is about 1,600 rpm., which produces a G-force that's slightly more than a larger-diameter TL or FL running at 800 to 1,000 rpm. As per above, if you try to get a flow-through rinse/extract (by sticking a plastic hose under the spin tub lid) you'll strain the spin motor (with the result that the spin tub runs slow and should be shut down and allowed to rest for about ten minutes). Instead, it uses the overflow rinse method, which I understand is fairly standard on Asian machines. Fill up the washtub, put in your clothes, turn on the agitator, run water through while it's going. The efficiency of this method depends on a) how much detergent you've used, and b) how much you've turned up the water from the faucet. This is an incentive to be conscientious about not overdosing on detergent during the wash cycle; when you get the dosage right, it won't take excessive water to rinse out.
Using the overflow method, I've found that it's possible -without using excessive amounts of water- to rinse out *all* of the detergent, so my clothes come out without even the slightest hint of detergent smell. Usually I rinse to a level where I can just barely smell the slight citrus smell of my detergent, since it's basically harmless and most people are used to having a slight detergent smell as an indication of clean clothes.
What else...? Weighs 70 lbs., has casters, easy to move around. Comes with a nifty quick-connect for your kitchen sink faucet.
One modification you might want to do. From the factory, the rear panel on the Danby is attached with screws to the rear of the metal housing of the machine. When it's running, this rear panel can be a source of vibration noise. What I did was unscrew the rear panel and run duct-tape around its entire perimeter, and fold the duct tape over so it covers both sides. (For example, if you have 2" wide duct tape, run it around at 1" from the edge, so the front edge has 1" of coverage, and an additional 1" of duct tape is exposed; then fold over that extra 1" so it covers an inch of the backside of the panel.) This also safely covers the otherwise somewhat sharp edges of this metal panel. Then I screwed the panel back on, and the duct-tape worked as planned: it provides a slight but sufficient layer between the removable panel and the metal housing, thereby eliminating that vibration noise. (You can make jokes about duct tape, but in this case it works wonders and doesn't look objectionable.)
Another thing you might want to try: If you discharge wash water into the sink, try putting the discharge hose over a fine-mesh strainer (same mesh as a tea strainer, but a full-size one). This will catch lint that would otherwise go into the sink.
Last but not least, get a decent measuring cup for detergent. I use something that looks like a "shot glass" that people use for drinking distilled spirits, except this one is calibrated in various units of measure: teaspoons, millilitres, ounces, etc. Keep track of your detergent usage and you'll find the right amount to get everything clean without overdosing, and thereby be able to keep the rinse cycles short and water usage efficient.
I think it's likely that twinnies will make a comeback in the US. Water and energy efficiency similar to a front-loader, at about half the price (the Danby unit goes for $250 - $300 depending on where you buy it), and without the well-known vibration issues of front-loaders. The latter point also makes it a good bet for apartment dwellers, since it won't disturb the neighbors. The internal layout looks clean enough that repairs should be fairly easy, and the mechanism is so simple that it should last as long as a more heavily-built machine.