Something is not right with the wiring. There should not be any significant voltage between the radio chassis and ground or the scope chassis and ground. That 36 volts is suspect to me. Man I hate giving advise to someone regarding AC wiring.
I am very comfortable tearing into an outlet to check the wiring but others may not be. I guess once you worked on 5000 volt DC supplies a little 120 ac outlet is a piece of cake. LOL All I can say is in the AC outlet the white wire (neutral) should go to the longer hole, the black wire (hot) should go to the shorter hole and the bare wire (ground) should connect to the outlet box itself or to the green terminal screw on the outlet itself. If the CB power supply has a two prong cord and the prongs are the same width, reverse the way it plugs into the outlet and measure again. If there is still no difference you may need to run a simple wire connecting the radio chassis, power supply chassis, and scope chassis together and tie it to ground. Then stand back and turn everything on. LOL No seriously sometimes you can have a phantom voltage floating around on the chassis and a common ground solves the issue however it is always better to solve the source of the issue first. I did have to install a common ground on a piece of tube type test gear one time to eliminate a similar issue.