Even in those examples with inappropriately shared neutrals and such, shouldn't a solid neutral connection to the neutral from the utility ensure that the neutral voltage at the entrance to the breaker panel is still good?The only place all neutral and ground circuits should be bonded is at the mains panel. 240 VAC appliances like a stove, drier, air conditioner or electric heaters should have their own L1, L2, Neutral and Ground at the load center. I have seen a few instances where on installation shortcuts where taken and later resulted in strange problems. Examples where a neutral for example was shared and should not have been. Things go along fine for years right till a bonded connection in a box somewhere gets overloaded or simple becomes loose with age. The trick to trouble shooting becomes trying to figure out which branch circuits go where which is a challenge since the wires are in walls.
My guess is the power company will show up again and run a load test at the point where their responsibility ends. Then the problem gets placed back in your lap. I don't see where the symptoms you have will be a result of a hot (L1 or L2) with a fault but think your symptoms point to a neutral. The problem lies in not actually seeing how everything is distributed in your residence.
Ron
I totally understand that there are a lot of ways for sketchy wiring to compromise individual circuits (or groups of related circuits sharing a common neutral,) but I don't see how any of that would push the neutral at the panel entrance around, unless there was a problem between the utility and the panel entrance.