Wait a minute. That's less than 4 tenths. Isn't that far better than the machine itself? Isn't anything less than 5 tenths considered pretty good for general machining?
If the Haimer isn't working for you what do you go with instead?
One option with electronic edge finders is to probe twice 180 degrees out, and then do the math. Even then unless you have a really really high end probe you could still be +/- a couple tenths. I've tested this by auto probing hole centers with am electronic probe. Cheap ones and mid range ones. Never had a high end one.