Hi Sven, welcome to CNC Zone.uk. Its nice to see our products assembled into a machine....
Y axis Ballscrew: For production purposes, to make the application cost effective you will need to use a 25x25 or 32x32 Ballscrew with a rotating Ballnut, cost £2500gbp lead-time 18 weeks.
Therefore I suggest a cheaper option: Rack and pinion; the pinion will require assembly to bespoke bearing block, as the stepper motor bearings are not designed to carry the extra load of the pinion.