My '71is not held in by a "U" clip it has a threaded lock cylinder and is held in but a large nut. It is a pain to tighten as it is inset behind the panel with a small access hole. My guess is you nut is loose.
I have used the replacement cylinder locks on other applications (gun safes, office mail boxes). If you can fit a large washer over the back of the cylinder before you tighten down the large nut it might help. Since the metal is thin in the back of the car the nut be tightening on is last thread which could cause some play. Hopefully I will be replacing my missing trunck lock this weekend. I will let you know how I do on this.
Those retaining nuts are a special design that has 4 cuts in each side so it can be tightened with a flat blade screwdriver through the access hole. Very similar design to conduit and junction box retaining nuts.