In all my years of working on heating can’t say I have ever noticed the radiator bracket being hot,be easy enough to remove rad ,slacken the brackets and put some of the reflective insulation foil that is available on the wall.
I would repipe completely ,I am old school and prefer copper but if doing yourself speed fit is a easy option,have new rads correctly sized for running at a lower temperature to keep your boiler in condensing mode as much as possible.
The valve body can pass, incorrectly piped ( has it just started doing this)have you a gate valve on the heating circuit after the valve? If so shut it and see if it still gets warm.