It's begun....

[JAZZCNC]

What voltage are you running those steppers at.?
How are motors wired, Series or parallel.?

Regards heat then steppers do get Hot can you hold your hand on them for a minute without burning you.? If so then they'll be fine. They can take much higher heat and still work ok it just shortens there life.! . . They would have to be very very hot to lockup.

Your problem will almost certainly be coming from that belt setup causing misalignment and binding. Being honest now your always going to struggle with that long extension like that on ball-screw without some proper sturdy support or holding fixture. Even then it will need to be aligned spot on.
I'd seriously look at running 2 motors . . or . . Dumping the existing motor bracket then have 2 pulleys on one screw with belt on one across to other with shorter belt on other pulley to motor. This way you could apply some gearing and keep the Nema 23 which should do this job ok provided you have decent amount of volts.

That size machine with 2 x 3Nm motors running decent volts even with 5mm pitch screws should be running easily 6mtr/min at minimum.
I built a very similar machine with probably heavier gantry for Michael Marino running 5mm pitch screws with 2 x 3nm motors on AM882 drives with approx 70Vdc and I'm pretty sure he's had it up in the dizzy heights of 16-17mtr/min when pushing for it's limits.!! . . . Sure he's regularly running it around 8-9mtr/min with high acceleration.!!

IMO dump that belt setup you have now it's a serious bottle neck.!! . . . .Use belts by all means but needs to be better setup than that.!!