Seems to be heat related as you say it clears up once the system's been on for a while. Heat expands metals, which would tend to make cold connections tighten up.
First things first though. Give all your tubes and sockets a good cleaning and re-tension the socket tangs. A slight twist of a small jeweler's screwdriver set between the metal and socket body works nice - it doesn't take much. Those will loosen up over time, and even more so when you're playing with them trying to fix a problem. I find that all tube pins aren't the same size either, so not a bad idea to test the sockets for tightness every time you swap.
You'll also want to be careful and precise when setting and removing tubes. No rocking allowed. Pull straight up, and push straight in, with firm, even pressure. You can tell when a socket's "right" ...
I'd also try swapping the interconnects first if you haven't already. Those go bad surprisingly often. Like the sockets, they should be a nice tight fit. RCA jacks can also loosen up over time and can be adjusted from the back using more or less the same process.