Hi Gustave - If a ballscrew works at your size then usually a ballscrew is better. They are available in cost/tolerance brackets are easy to set up and get to work.
A R&P gearset is designed for gear clearance. It's actually poor mechanics to have a system that pushes the two together. But DIY and others do not have the machines that can cut ways and registers to set the pinion/rack at the correct clearance so they use springs to deal with this issue. At a certain length or speed screws become problematic so then R&P takes over for "long" distances. Soon linear motors will take this over, they are available but too costly for the hobbyists.
Its your 1800mm that will be the issue with screws so look at the suppliers design sheets and that will determine if the 1800mm will work for you. Maybe the small axis are screws and the 1800mm is R&P .. Cheers Peter