I don't think you can draw much information from the LEDs. My Y motors stay in sync and the LEDs sometimes seem to flash together, sometimes not. I get more noise on the "J" file you sent on the slow curves at the bottom. The Y motors resonate the end plates and gantry with they are slowly stepping. the rate change around the curve makes a strange musical sound. If the spindle is on, you won't notice. You should be able to apply significant resistance to the movement of the machine as it follows your gcode. The steppers are very strong.
Its funny you mention the musical sound. I am getting it now too I wish I could figure out why it is doing it but as you say, it is moving correctly. I do appreciate your help on this, I would have never believed it was the gcode causing the biggest issues. I am sure the underpowered power supply didn't help either (thx Robert).
I'm glad we figured it out. I wouldn't worry about the sound. It's normal for many stepper driven machines to make music. My delta 3D printer does the same thing. It's just the changing frequencies of stepper pulses creating 2D or 3D movement. Happy cutting!