The linear position feedback devices I have seen are always far less accurate that the resolver off the motor. This is fine when you don't need that much accuracy, but is difficult when you want to do something fiddly like get rid of your backlash.
The main solutions that I have seen is to compensate for the backlash somehow.
First you have to decide what is acceptable for your operation. If you can somehow get the backlash down to a level where it doesn't matter, that would be best.
So, here are my ideas:
1, The best ball screws have little backlash between the screw and the nut. Therefore, you may be able to just run an encoder directly off the screw as some other posters have suggested. If this is not good enough, then it can be combined with other methods.
2, Drive your load in one direction only. If you need to drive the load in the opposite direction, overshoot by a distance in excess of the backlash, then drive it back in that direction. It is best if you load has a bit of resistance to movement of some sort of damping, to prevent it from ending up in a random location within the backlash band. This compensates for the backlash by ensuring that it applies in a determanistic manner.
3, Use backlash compensation calculations. Some servo drives have these built in, or if not you will have to create these yourself. You must calculate the magnitude of the backlash, and feed it into your calculations. Note with this method that mechanical wear will increase backlash over time.