Ok well lets see the rest of the design for Z axis and work from that.

My suggestion for nema 34 on 2020 screws was mostly for the long (X)axis to keep screw speed down to reduce whip and still maintain 10mm pitch speeds but I've just noticed it looks like your intending to use rotating ballnuts which if correct then you could use nema 23 motors on 10mm pitch.
That said 20mm pitch would allow a ratio to increase torque and have a lower nut speed for same speed as 10mm pitch which if using 20mm dia screws (which I would use at this length) may be better with the larger nut on smaller motors.

This doesn't help the Y axis thou which will still need nema34 motor if you use twin screws on single motor. That said Mixing motor sizes isn't a problem if you use High powered drives because they run from mains AC so don't have a mix matched DC power supply which would be needed for the lower voltage DC drives running the nema23 motors.