A few years back I had this exact problem. I'm not at my unit, but I believe it was the one that was had on on/off switch for the Wingard antenna.
I called Wingard, explained the problem, which they are aware of, and they sent me a replacement plug/plate thing. Still a tight fit but better. I don't use that 12v. socket for much of anything anyway.
Give Wingard(?) a call.
Sometimes I wish I were living in the stone age. Then I would know I'm the smartest person in the world.