Hmmm, the search for the perfect square cut on the shopsmith. I have been through that search myself!
I have the Incra miter guage v120 for the shopsmith and it works great once squared off to the blade for a variety of angled cuts.
However, I am able to achieve the needed 90 degree square cuts with the normal shopsmith miter guage as well. It becomes a bit more of a hassle to achieve different angled cuts reliably using the normal shopsmith miter guage.
I have used a similar technique to you, but with some variation.
A couple of things.
Is the table perfectly perpendicular to the blade as guided by your square. Is the blade warped in any way? Is there excess vibration? Is the arbor shifting or slipping on the hub even a tad bit. With a cut being 1/16" out of square at times, that's pretty huge deviation on a 4" width cut so there seems to be major movement somewhere.
You can square the blade to the miter guage slots (I use a woodpecker saw guage dial indicator for this), but I have found that simply using a quality and dependable square (I use a woodpecker square Model 851) works well to square the miter guage to the blade. I just hold the square firmly against the miter guage and then gently lay the square flat across the blade (so there is no space between blade and square) and then secure the miter guage at that spot. That will usually yield a perfect square cut as long as there is no blade deflection, excessive machine vibration or run out issues from failing bearings. And if it doesn't then simply adjust to square based off of the angle of your cut by simply taking that same square and adjusting it slightly off the blade at the angle needed to correct to get square and reset the miter guage and just play with it until you've achieved square. Actually, it takes a little time, but it works for me. So, if for some reason square is not achieved by laying the square flat against the blade, then you'll need to adjust the miter guage one way or the other to achieve a square cut and it doesn't necessarily mean that the square will actually be perfectly square to the blade and miter guage. For some reason, as long as whatever is causing your cut to not be square is stable, you can achieve square cuts this way. If the anomaly is not stable, then you have to find out what the root issue is or you'll never get square cuts.
Cheers,
John