I'm an RF technician myself who has swept thousands of antennas but I don't have experience sweeping antennas in the AM/FM range that our radios use.
The ground plane is absolutely vital for transmitting and while it's important for receiving, it's not nearly as important. In our field, we always say you need your antenna dialed in to be able to transmit correctly but you can basically receive with a coat hanger. I've tested plenty of antennas with pretty sketchy ground planes and it really just depends on the antenna, the frequency and whether or not you can manipulate the attachment to make the ground plane better.
In this case, I'm curious if @70Duster340 tried my suggestion and just ran a couple alligator clips from the base of the antenna to good grounds on the chassis to see if that would wake the antenna up and allow the radio stations to come in.