Re: gearing.
1:2 or 2:1.

1600 rpm for a nema 34 stepper sounds extremely high.
Typical is 800 rpm, or less.
4m/min = 66 mm/sec.
A 5 mm screw at 1:2 = 10 mm per rev of motor.
So 12 Nm /2 == 6Nm stall and maybe 3 Nm 300 rpm.

At 1:2 you would have half the torque vs direct gearing.

For 10 mm /rev, 4000 mm/min = 400 revs/min.
6.6 rps.

Anyway, if as You said the threading ignores acceleration settings, then maybe / probably the problem is lack of torque on z past 200 rpm at spindle.
The z axis tries to accelerate to a speed suitable for the spindle rpm, and cannot do it.
The z axis maybe tries to accelerate "instantly" to the required sync speed, and simply does not have enough torque to get there before stalling.

If gearing 1:2 motor/screw your screw would run at 3200 rpm at 1600 from stepper.
That is probably wrong.
2:1 is probably right.

Anyway 4m/min on a medium lathe like yours, and gibs, is far too fast.
It will wear out your mechanicals real fast.

My lathe is about the same size, 12x24.
On servos with 10x the acceleration and 5x the speed my rapids are much lower on purpose.