Yes, in this case, it sounds like you need the following circuit
1) leave mains earth connected to the chassis, for safety reasons.
2) turn on the Y capacitors, which filter, after a time delay
turn off is more troublesome, you would need to disconnect the caps before turning off, then connect them. Pain in the ass since you need mechanical sequencing or a super cap
or
get a RCD that is industrial, which has a greater trip requirement (but is dangerous)
or
add some resistors between the Y caps and the circuit to limit current.
Your safety is #1, the EMI performance of the thing only matters to legislative bodies.
your Y caps I think basically offer a better path for energy then radiation resistance
*****
personally, I just have a non GFIC outlet in my lab, for unruly devices I don't use often. Some of my microwave amps trigger them.