Do you realize that lead-acid car batteries supply 12.6VDC when disconnected from the car, or 13.7VDC to 14.7VDC when connected to a running car, at enough current to make your OBi explode if it was defective, and there wasn't a fuse in the circuit? At least it didn't fry your OBi.
If the old OBi doesn't cause hum, and the new one(s) do, then contact Obihai.
Have you tried using a telephone which doesn't have its own AC/DC power supply? In other words, a bare-bones, single-line, wired telephone? It sounds like you have a ground loop between the phone and the OBi. There are filters available to block this, but you should try to identify the underlying cause. If you can take the OBi and a basic telephone to another building, it would be worth testing it that way, too.