I'd think that a floating plate intimately connected to
switching devices (mechanically, if not electrically)
would be mysterious at best, capacitively coupled
to busy bits and hence an EM radiator most likely.
What about putting high voltage, low ESL/ESR caps
from these plates to the case ground, to at least
shunt-divide any such HF that may be riding on the
plates?
Have you put a "sniffer" to the plates to look for
EMI magnitude? That would tend to answer, or at
least bound the problem.