My Goodness, What A Thread.
Here is my take on the whole thing. In the 80's I used to have an old 60's Speed Queen set (solid tub of course) and I believe SQ and Frigidaire (and some others) had a good idea with the overflow rinse. It seemed to work a little better on the SQ's because the fins on the agitator seemed to push the suds toward the o/f better than the chaser ring. Can't say that for sure because I didn't ever have one, but from what I've read on here over the years, SQ seemed to do a better job of pushing away the suds.
When I had my SQ, by the time the spin started all the suds were gone and the water was clear, but that was before I had a w/s, which would make a difference in the amount of suds; always does. One uses less soap in soft water. As far as sand, we didn't work on a farm. The most we did was work in the yard; mostly mowing. By the end of the cycle the clothes were very clean and soap free, as far as we could tell. Very smooth and soft and not much smell at all. We had a gay girl living with us at the time and sometimes she would come in very dirty. Her clothes always came out clean too. That SQ didn't have a very big capacity, but sometimes I really miss it. It was such a cool machine. What did it in was when the solenoid would bang up to engage the drive block, the block would slip in and out and the machine would have intermittent agitation. Unfortunately I didn't try to fix the problem and just threw out the machine, which I really regret now. I had a business to run and other things on my mind and I thought there would be other machines out there to purchase that would be just a good. I was in for a big disappointment.
In my current Maytag experiences, the results are about the same, except if I put too much soap in the wash the rinsing isn't as good, as we have soft water now. Launderess is correct that rinsing seems better in harder water, but according to tests done on this site by other members, that can be deceiving. The hard water seems like it's rinsing better because it suppresses sudsing action, but the suds may still be there. Even in the sink when I try to rinse dish liquid out of the dish cloth and down the drain, it takes much longer to rinse the suds away. In hard water I think it may still be there but doesn't show itself. I don't know how else to justify this phenomenon. Anyway, this summer when our w/h was a complete disaster, I had purchased and 80's BOL Maytag to steal the trans and agitator out of for a rebuild of an older series 0. Since It was on the patio and I had hoses for hot and cold water, I manually filled the machine and washed outside. I felt like a woman on wash day 50 years ago. When it came time for the spray rinse I would turn the cold water hose up on full blast and spray the clothes for nearly the whole spin cycle. By the time it was over the water coming out of the drain hose was completely clear. If the Maytag would spray a large volume of water for the whole wash spin, I believe the results would be better. But this might run up a water bill quite a bit. It certainly gave good results.
Back to the solid tub machines. I have never had a problem with them and I was always please with the results. I was always amazed at how dry the clothes would come out with no perforations in the tub and sand was never a problem for us. I guess it depends on ones living situations.