If you're VERY careful, you can get a better connection by lightly scraping
the pins with a dull knife. This helps to remove some of the oxide.

Also, carefully spread the pins outward just a skosh with long-nosed pliers.
This gives the pins a better grip in the socket.

BTW -- Are you sure that the solder connections on the CRT socket are OK?
That's often a weak spot. Resoldering those joints will often help.