I'm an EE/PE and agree with the advice cited. Safety first

If the cheater plug is the solution, there's likely a wiring deficiency (broken ground, neutral/hot reversal) in your electrical system that's an accident waiting to happen

Have a licensed electrician inspect your wiring or check it using an outlet check plug readily available from Home Despot, Lowe's, Menards, etc.
As for the buzz, start with the basics. Turn off the power amp(s) and disconnect the interconnects from Tempest to PA. Does the buzz remain? If so, you have a spastic transformer or relay in the Tempest or a relay power supply that's lost its filtration; your buzz is mechanical! Send to Indy for fix.
If the buzz went away with the power amp(s) off, restore power to the PA(s), but leave the interconnects from the Tempest disconnected. If the buzz returns, it's likely in the power amp(s), either a filter capacitor or rectifier diode failure.
Next, ensure that the Tempest volume control is fully counterclockwise and that the Tempest and PA power switches are off, but their power cords remain energized. Disconnect all inputs from the Tempest, restoring only the interconnects to the PA (Stratos?) and energizing only the PA. If the buzz is appears, you likely have an input interconnect ground fault. Replace interconnects.
If the buzz is gone with the Tempest off, but present with the Tempest on, it's a Tempest problem, most likely an internal connection fault but possibly a filter capacitor and/or rectifier problem. Either way, return to Indy for fix.
If the buzz returns only when you connect your sources to the Tempest, then you have either a source or source-Tempest interconnect fault.
Another means of checking the Tempest directly is to shut down your PAs, disconnect the Tempest-PA cables, and connect headphones directly to the Tempest output. Go to Radio Shack and obtain a RCA plug to headphone jack adapter. Using a set of higher-impedance headphones (e.g., Sennheisers, Beyers, or AKGs), plug the headphones into the Tempest output jack(s) using the adapter. At low volume levels, you will do no harm to the Tempest by this connection. If you hear the buzz via the cans, with no source connections to the Tempest, the latter is faulty.
Hope this helps,
Karl