Because this is a whole house issue, it reduces it to essentially the connection to the main breaker/ground. And something outside with the utility company.
I like the idea that it might be a poor ground connection.
As far as whether that could cause over-voltages, I played around a few years ago with 220V and a floating center ground. It was rather odd, but yes, a load on one side could throw the voltage on the other side wonky.
Now, diagnosing on your end. It will depend a bit if you are comfortable with the main breaker box.
One relatively safe diagnostic you could use would be an IR camera or IR thermometer. When you're running a heavy appliance (for a while), then a shorted connection would likely show up as a hot spot in the box. Primarily concentrating on the big wires at the top, or the bus bars.
A floating ground would show up if you turned off most stuff in the house, then turned on a single 110V high power device (1500W hair dryer?) Checking your breaker box with an electrical tester, then every other breaker would be high or low.
