Re. indexing:
At risk of being unpopular, I'm going to say it shouldn't make a difference in the water currents.
Reason is this: Water is dense, has a lot of inertia. The smooth sides of a tub, when rotating during indexing, can't get "traction" on the water to make the mass of water move with them. To check this out, get a bucket full of water and rotate it back and forth by holding it off the ground and turning the handle clockwise and then counterclockwise. Drop a single square of clean toilet tissue in there so you can see what's happening. Nothing will happen; the water won't move much, the bucket will just "slide" past the water in each direction.
Now you put an agitator at the bottom and it's going to be moving faster than the water can move with it. So it acts like the impeller of a centrifugal pump and throws the water outward at the base of the agitator. The water current hits the side of the tub and turns upward, in a toroidal shape. The vector of the inertial mass of the water is perpendicular to the agitator. There's a lot of mass moving fairly quickly there. That mass is not going to be affected much if at all, by whether the wall of the washtub is or isn't moving.
Now let's take another extreme case, and assume we have a vertical-axis washtub with an agitator in the center, and the washtub itself has vertical blades in it like the tub of a front-loader. Now we'll have that hypothetical washtub index back and forth, and to be even more extreme, we'll have it move *in unison with the agitator.* In that case what we're going to get is centrifugal force (angular momentum), where the mass of water is really being pushed around and tries to climb the wall of the washtub. But the speed of the agitator is calculated such that there is not enough centrifugal force to cause the water to slosh out over the top of the washtub.
If you were to look at a cross-section, what you'd see is that the top surface of the mass of water is roughly concave, slightly depressed at the center and slightly higher at the edges. And if you were to throw in the hypothetical piece of clean toilet paper, or a handkerchief or washcloth, you'd see it circulating in a toroidal pattern: the water that has reached as far up as it's going to get along the walls of the tub has to go somewhere, so it rolls back down toward the center of the tub and then follows the column of the agitator downward to start over again.
I somewhat doubt that this hypothetical configuration would wash very well because the load would not be moving in a circle (the circle surrounding the axis of the agitator). It would only move in a rolling-over motion, no circular motion for mixing, so the large and small articles would tend to segregate in the load. You'd get a lot of turbulence at the periphery and that would produce excessive wear on some of the clothes.
It would be tempting to suggest that this configuration would wash fine if you used a shorter washing period, since after all, Hoovermatic used a maximum 4-minute cycle. However, the lack of mixing would produce the result that some articles would come clean and get a bit of excess wear in the process, and some articles would not get enough movement to get as clean.
Anyone wants to try this badly enough, there is probably a way to build a working model to test these ideas.