Sam,
1500/(16*12) = 7.8 ft lbs. This is not a huge amount of torque. By comparison, you can think of tightening up a 1/2" wheel stud to what, 50 ft lbs? Normal cutting action, even at high feedrate will not hurt it.
The high momentum of the spinning screw moving a heavy load (in rapid mode) can have completely different effects, though. The screw could get bent in the event of an accident.
Also, another option is to limit the current gain on your servo amplifiers so that they trip out before the motor reaches its peak draw. However, this will affect your accel/decel ramps in a negative way. But, this might be an option while you are in the startup stages, and are just test driving your machine.
Yes, small screws are more likely to vibrate and shake at high rpms.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)