I'm no engineer but conceptually it would appear that axial play on a ballscrew is totally irrelevant if the linear guides are doing their job properly.
Therefore, assuming that there is no axial play from the linear guides, the only error potential left is backlash and if the ballscrew has zero backlash, then you've got a fully functional solution.
Removing axial play from the linear guides is a separate problem to this thread and will have certainly have been covered elsewhere in threads that talk about skew and torsional forces, etc.
I'd personally ignore the ballscrew axial play as it should be engineered out via linear guide design / construction.
Any engineers out there able to add to this opinion?
Andy
Drat, imperfection has finally stopped working!!