Randy,
That vise is basically a drill press vise, not a milling vise. It doesn't look like it "pulls down" when tightened to prevent jaw lift, thus tilting the part. That is probably what is causing the inaccuracy. If you draw file the sides before hand billet stock is usually pretty flat and square.
A good alternative would be a precision screw-less vise. They come in a variety of sizes (3" jaw width would work well) are square and flat on all sides and pull down to prevent lift. The downsides are an allen key is needed to tighten/loosen them and they don't provide the clamping force of a Kurt style vise. For the size of machine this limited clamping force will not be a problem.
Also, they don't have separate jaws so soft-jaws are out of the question.
If you go this route be sure to get one(s) with clamping slots on the sides and tapped holes in the solid jaw to mount a stop.
Thanks for all the pics,
Serge