Hi,

I think the only practical solution for a 1800mm Axis is to fix the ballscrew and drive the nut.
This is rather expensive but you get a very fast and dynamic machine and a 20mm Ballscrew will be OK.
(I have a >2000mm Axis with a 16mm ballscrew - but this is a foam cutter with low requirements - the spindle bends quite a bit even though it is fixed at both ends and put under moderate tension)

If you drive the ballscrew as usual you'll need something about 30mm diameter to get any reasonable speed - but this will still be very very low dynamic due to the spindles high inertia.

Christian