My cross slide has over 10thou of backlash just now, but it doesn't cause me many problems. You've just got to compensate for backlash, and realise what you can and can't do.

Looking at the diagram you've got, it looks as though you're planning on controlling endfloat by using a bearing at each end, and then preloading the entire ball screw. If you are, it's not a good way to do it, as due to expansion/contraction of the various components, things can get deformed.
You should control endfloat by having one end of the ballscrew fixed (ie. a couple double angular contact bearings to set endfloat) and the other floating (ie. either a bearing that supports the screw but allows it to slide through it, or a sliding coupling if you're using the stepper motor to support the shaft).