I'm now looking at direct drive, a 17t pinion will give me 53.39mm of travel so I will need 168rpm to reach my top speed of 9000mm/min.

The gantry will weigh at a guesstimate 30kg and will have two 3.1Nm motors, direct driving it.

This might work better as it keeps the motor rpm way down in the high torque area.

Any chance you could illustrate the maths needed for the acceleration estimates???