Again, late to this party.
Long story short, it seems to me that if a baler takes in an adequate charge of hay to uniformly fill the bale chamber with each plunger stroke, you are going to get a consistently square bale. That assumes the charge of hay is left in the middle of the chamber to spread evenly when it is compressed .....side to side and top to bottom.
In a former life, I ran a JD 336......can't ever remember any bad shaped bales. I've recently ran an older Massey baler and we had trouble with it. I currently have a NH 315.........and most of the time, it spits out bricks. That is when I've got decent hay and the windrows are consistent. That is not always the case........and do get the occasional funky bale. One side a bit longer.....or more unusual.......a concave bale.......bottom longer than the top. What gives?
A few years back, I attempted to bale hay with Massey Ferguson #9......a small entry level baler. In dry hay, we could never get it to do better than 40# cotton balls......then realized it didn't have any wedges. Actually, what Massey called a "retarder" plate, which is along the line of what JD uses and is different than the wedges NH uses. The "retarder" is a plate with grid of half moon pockets projecting into bale chamber. I can't imagine how bale skiis would improve on those.
Anyway, once you really start to evaluate balers, there are some subtle but significant differences in only a few places. For example, JD uses an auger to move hay from the pickup to the mouth of the bale chamber. That is a continuous flow.......and what hay you have stacks up right there, waiting for the packer fingers to pull it in. Stacks up pretty evenly. The JD's also have the retarder plate vs. the wedges (at least the older ones do).
Almost all other balers, including the New Hollands, use tines to move the hay sideways in a start stop motion. As long as the charge of hay with each plunger stroke is big enough to fill the chamber, and the packer fingers are timed right to leave it in the middle of the chamber........and not off to the far side......or just barely inside.......you get a decent shaped bale. I think this is the reason most guys will say a NH baler does best when you feed it heavy. It is getting a full charge of hay with each plunger stroke. So I think the NH and similar balers are more sensitive to the charge per stroke.....and that is tied to the feeding mechanism.....an auger vs. the tines.
After that, timing of the delivery factors in.......and on my NH 315, I can even adjust a baffle at the back of the pickup chamber to account for windrow size. Who does that? In theory, however, as per the book, that is an adjustment to make that will affect bale shape. Most of us do that on the fly by adjusting ground speed.
But back to the OP's issue with the 5070........I doubt the size of the material is as important as the amount of material you are running in with each stroke. My rule of thumb is to vary windrow size and speed until I can get flakes that average about 2 to 2.5 " in length. That means I'm getting a nice charge of hay with each stroke. Goal is about 15 flakes +/- per bale. Larger than that and I'm pushing it too hard........less and no telling what will happen.
Last baling, I double raked one field to get a nice windrow. Another field was light and I put 8 windrows together to make the same size. It wasn't worth baling.....but did it to clean up the field. Both made the same size and shape bales, although the latter were a bit funky on the corners as the material was very short.
My goal is to make 50# bricks. It took a bit of trial and error to figure out how to do that, but I do it by using 2 wedges, cranking down the tension and shortening the bale to about 30 to 32 inches. Drop one of those on a flatbed and it sounds like you dropped a cement block.