Your backlash issue is not uncommon at all and is a major factor in either choosing the quality of a machine to start with or limiting the precision of the parts that are manufactured. The conversion of a milling machine to a CNC machine is a waste of time without due consideration to the lead screws and their backlash. Acme threads are available in increasing grades of precision but the nut is a 'wear out' part and is constantly adjusted for backlash. Ballscrews with preloaded nuts are the standard for CNC but even they have limitations and degrees of precision and usually their mounting will be a factor in backlash. Point being: your awareness to the limitations of a machine and the ability to compensate is a common thing that we just have to deal with...
Sounds like an interesting pursuit...
BClem