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I did a lot more testing to locate the source of the sound today.
Like I suspected, it was related to the motor for the Y-axis driving the bed back and forth.
I made a small test macro that moves the bed back and forth a few times and a fixed speed, with max acceleration. The areas marked with red squares in the images below is when it was moving the Y-axis alone on full speed (175mm/s in the test)
I did some light frequency analysis to see which frequencies were actually the issue, and the excessive noise seems to be around 200Hz.
Loudness of this is somewhat affected by the tightness of the belt, but not in a significant way. But even with the belt and bed disconnected from the motor, the sound remains almost unchanged in loudness.
I unmounted the Y-axis motor from the frame and printer and placed it on a vibration-dampening mat and performed the same test again.
It clearly shows the 200Hz sound is originating in the stepper, red boxes in the image above mark the Y-axis movement. It shows the vibrations at approx. 200Hz, but at a much lower level.
so it would seem that it is more or less the frame that amplifies the motor vibration to an excessively audible level.
Next step in this is going attempting to mechanically disconnect the motor from the frame with some dampeners and rubber washers and see if that will help significantly.