Wish I had a torque-speed curve to illustrate that those servos will far exceed steppers performance-wise but you absolutely must gear them down. 4:1 ratio would allow over 200IPM rapids on 5mm lead ballscrews and provide 200/1400oz-in continuous/peak torque over the majority of that speed range. By comparison, a direct drive 370oz-in stepper would give comparable rapid speed but only maybe 50oz-in torque availabe at higher speed range.

As for belts, trapezoidal shapes such as M, L or XL designations are prone to backlash because the trapezoidal shape requires extra clearance to allow the belt tooth to enter the pulley slot when rotating. Curvilinear belts such as GT or HTD are shape optimized to allow meshing with little to no clearance required. Last time I priced pulleys Timing Belt Pulleys & Timing Belts - Power Transmission Components - Synchronous Drive Parts | B&B Manufacturing had pretty good pricing and selection.

There's a surprising amount of flex in those RM series "anti-backlash" ballscrews - I got the 20mm versions and still crave more rigidity. Two ballnuts preloaded against eachother would probably do it and the nuts are so cheap it's not worth the time to experiment with oversized balls.