the only connection to the inverter is the output of the DAC to give speed command to the inverter
That means that you have a common ground.

When I worked with inverters, we needed, when testing, to locate the tacho several feet from the inverter to ge a RPM reading.

1) Are you far enough away to not have radiated noise, try 100 feet.
2) While staying away as in 1) for the sake of verification, replace the DAC output with a voltage from a battery and a couple of resistors (potentiometer) or such. This will give the chance to see if the wires from the DAC is the culpit.
3) If 2) makes the noise effects disappear, keep the battry and connect the ground/return wire from the DAC ONLY.
4) if 1) does not fix the problem but 2) or 3) does, keep the rig as in 2) or 3) (the one that works) and move closer to seee if the radiated noise is still a problem.

Try the above and come back, I am 97.23% convinced it is one of the above. When you have determined which, I'll have a handful of ideas.

Erik

Ps "the only connection to the inverter", do you have other connetions to the motor area (tachometer or such?), this includes other connetions located in the motor area (such as a tacho not electrically connected to the motor).