I cannot understand your problem with backlash. Mach3 deals with backlash perfectly. I have a cheap lathe which has quite a lot of backlash. This summer I will deal with it, and probably put in ball screws - but until then Mach 3 deals with it and it is accurate to the thousanth of an inch.
You would be able to, I am sure, deal with backlash on a manual machine, I think we have all done that at one time or another - on Mach3 it is just the same, but the computer does it for you.
All backlash is is the non-movement of the "table" whilst the gears, belts etc etc settle down to pulling the other way.
On any system, to check it - use typed gCode commands, switch off backlash compensation - move one way - stop, set measure to 0 - move same way for some distance ( the distance does not matter,because backlash has nothing to do with distance, but you can say move one inch and check the table is moving accurately) - stop - reverse back to start.
Your measure should now read 0 - but it will not - this is backlash. Enter it in the table and switch on backlash compensation.
It is simple and accurate and all mechanical systems must have it, otherwise they would seize up - it is only when it gets big enough to notice it becomes a problem.
The only problem I can see with a rotary table is measuring the backlash - I have things to measure to a thou, but nothing that will measure to a degreee (accurately). I suppose you could convert to thous and then convert back - it depends on how you set up the axis.