You could always use more powerful Stepper motors to negate the loss of torque at higher rpm. Also you could simply run your machine with higher rapids using servos so less of a gear reduction is required. 10mm pitch 10m/min rapids and a 3:1 reduction doesn't sound too bad! Ball screws have a maximum rotation speed so make sure you're not going to be over rotating them. 1,000 rpm is a pretty conservative speed but just be careful when it comes to spinning long ball screws at higher rpm.

If you'll be happy running at 3m/min then Open Loop Steppers will be a good choice. Rpm and microstepping both change the available torque so it'll be best to work out what torque will be required and choose the motor based on your calculations.

Cheers,

Fenza