MKJames
Well it seems you have replaced the power tube socket while connections and continuity has been looked at as well if I understood correctly but the problem remains.
This may be more of a pain but can be done without wait. As Anitoli has pointed out it may be a grid or screen resisitor acting up when temperature has increased and it should not go beyond those components because it only affects that one power tube socket in a four tube push-pull. So swap both the 5.6k grid and 1k screen resistor of that socket with another to see if the issue follows. If it does then then take VDC mesurements to see how it differs from the other three tubes/sockets. Replace the suspicious component if found.