Everybody seems to think they know more about the issue than the people experiencing it ...
We have contacted Solidoodle on this issue. They assure us that we are just messing up the belt tension. Or that our rod isn't aligned properly. Or that our VREF is off. Or that we're missing sometning else obvious. But let me tell you. I've spent a lot of time on this issue and I very confident in my printer's calibration. I was able to print the parts for the lawsy carriage tonight while I worked. I may not be able to print circles, but my prints are mostly fine. See attached images. This should prove to you that our problem is not typical! Poor circles usually results in many other defects, but the only problem I really have is sloppy corners and slightly non-uniform circles.
Our approach is not inefficient. If we knew of a better solution we'd obviously be doing it. Nothing is alleviating our issues with Y backlash.
It seems we are now deviating in 2 different directions to solve the problem. Jaques seems confident in his ability to design a part to test the 2 points of contact theory. I am going to upgrade to the lawsy carriage. I just dropped about $70 on all the parts. I am replacing every single rod, even the back Y rod.
If either solution results in better circles, we will know this is a design flaw. The SD4 has been filled with them so far; my first real snag was the spring for the extruder being too short and preventing me from using any other filament but Solidoodle's (Octave seems to be more slippery). There are many others I won't dive into, some of which I can't even remember. I see no reason to forfeit the assumption that this is a design flaw.
My parts for the carriages should show up in a few days. When they do, I'll rip out the old rods and carriages, get the hardware store to cut the new rods to size, and install the new carriages and see where I'm at. I will be completely FLOORED if this doesn't fix it, but I bet you it does.
Edit: picture only shows the Y carriage pieces but I'm also replacing X to be thorough. I could get away with just replacing Y, maybe, but I don't want to destroy the old carriages if I can avoid it. First time printing at 100% infill. 
I'm slowly going broke solving this issue. I've almost put the value of the SD4 into it now. Granted, not all my upgrades are related to this issue, but this should give you some idea of what's going on. Our issue is not trivial or typical.
While I wait for parts my side project is to design a replacement Z end stop block. Prior designs for the SD3 don't work on the SD4 because the holes were moved slightly to the left. I've already got most of it done, just need a couple more measurements. I'm motivated to do this because you other SD4 users can't upgrade to the e3d without hacking your endstop like I did to temporarily allow me to print. My hack sucks. I have to balance the bed every print because my endstop screw jiggles. Lol
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