Stepper motor CNC shield accelstepper.h

I believe that what you are seeing in both of those videos is the effect of resonance. Undamped steppers running at full steps (no microstepping) suffer from resonance. See this page. I had to set my drivers to, at least, x2 to get smooth running while testing the code that I posted. I usually run x4 to x16 in my applications. Most of the motors that I have resonate at 200 steps/second (full steps), right where your speed is.

So I suggest that you set the drivers to microstepping at x4 (quarter step) and adjust the steps and speeds in the arrays accordingly.

MS1 MS2 MS3 Microstep Resolution
Low Low Low Full step
High Low Low Half step
Low High Low Quarter step
High High Low Eighth step
High High High Sixteenth step

low is no jumper, high is jumper in place.