Why have you not use angular contact?.
Do it once, do it right.
You shouldn't need to shim anything if you have the ballscrew, bearings, nut set up right.
How have you put the bearings in?. Do you have a stopper ridge central inside the mount and then a bearing each side?.
This will allow the bearings to press back to back as the nut is tightened thus eliminating play.
If it is set up like this above and the nut is correct, then that's your backlash I'm afraid.