Yes, you do have it now. Sorry it took so long to explain it coherently. There are several variables, and you named one of them; that as the yarn gets thicker on the drum, it takes more yarn to make a single revolution around the drum. However, unless the thickness of the yarn increases or decreases, precisely the same number of revolutions will be required to move from point A to point B on layer 1 as it will take to move from point B to point A on layer 8.
Another variable is the thickness of a single ply. In GB, AU, NZ, and most if not all of Europe for that matter, ply has a specific meaning. So, the yarn we call "baby yarn", or "sock yarn" here in the states, is called "4 ply" in much of the rest of the world. We call it "worsted weight", most everyone else calls it "8 ply". Same word, same topic, but very different meaning. To further complicate things, there is no exacting standard. One mill might produce a worsted weight yarn that another mill down river a mile calls DK weight.
Folks in the US have invented a new wheel. It's called wraps per inch, or WPI. Ostensibly, it dares to set a standard. By wrapping a yarn around a ruler, and counting the wraps between any two inch marks, worshipers of the WPI standard can tell you in no uncertain terms what the weight of a yarn is. Unless they're pissed, wrap a little more tightly than usual, and cram an extra couple of wraps in there, or unless the individual who did the wraps was your demure gramma who wraps considerably more loosely than the average fiber artist because she knows not to ever wind yarn too tightly lest you stretch the life out of it.
Because precision on that level is impossible, I wouldn't mind if there was a half a yarn width gap between revolutions, or if there were an overlap of half a yarn width or more. Consistency is the goal, and it's also a very good reason to mechanize that aspect. You hit on a very important point when you said,
As you change the speed of the drum, you want to also increase the speed of the side to side movement.
Exactly right. And since the crank that turns the drum needs to be done by hand to respond immediately when something is amiss, creating an electronic component may possibly be counter productive. I wish it were as simple as adding 2 more pulleys and a belt connected to the existing power train, but I don't think it is because of the direction change that is required.
Anyway, thanks; good thinking!