Hmmm...

1:1 on to a 5mm pitch gives you a mechanical advantage of 1256:1

So 3Nm gives a driving force of 3 x 1256 = 3768 N

Question is, do you really need 0.37 tons to drive your Z? Using a 16mm screw suggests you are not lifting the bed.

Is it too late to change motors? I suspect you are severely limiting your top speed.

If you geared it 5:4 then it would half step .01 mm and quarter step at 5 microns which is my favourite, being the resolution of my digi calipers.