Sorry, I was sidetracked! The UPS I linked to was for informational purposes only. I'm sure you can find a less expensive unit.
AudioGuru66 is correct in what he says about what a UPS does. In audio you would be using it as a way to provide a clean, pure sine wave. It would clean any extraneous noise induced before the UPS. I'm not concerned about keeping the audio system running for just 5 minutes after power loss.
The transformer you are talking could be the culprit! It shouldn't be making the sound your saying it is. It might be time for a replacement. They are inexpensive and can be bought at Home Depot, or any hardware store. Shut the circuit breaker off and remove the wire feeding the transformer and see if this works.
That's exactly what the electrician did to the ground wires! So long as the connector is tight and the wires don't easily pull out of it, it should be fine.
As I'm typing a thought came into my head. In most panel installations in houses the grounds and the neutrals,(white wire), land on the same bus. This bus is supposed to have a green screw driven through it into the circuit breaker cabinet. If the ground wires are separate from the neutrals, then either the same screw is used or a wire jumping between the 2 connection points is required. The neutral and the ground in a panel MUST be attached!!!
If you take your meter and check the resistance between the neutral and ground it should read "0"
Hope this helps. Jim
P.S. Be careful in the panel!!!!