2.2:1 ratio would give you 200 IPM at your current stepper RPM. So any pulley combination that would give you somewhere around that ratio would reach that goal. Just set the steps per to match the new ratio.
Now the question: Does the stepper have enough torque to drive the system at that speed? I don't know. In general a NEMA 23 sounds a bit light for the task, but I tend to over power axis drives, you can always turn them down a bit. The torque of a stepper motor drops off rapidly as the RPM increases, so keeping it in the lower end of it's RPM range is better.
Given that this is a machine in commercial use, I would be tempted to repower it with AC servo motors, maybe in the 400W to 750W range, and be completely done with the problem. Yes, it will cost a bit more, but the increase in productivity will make up for it in the long run.