If anything, try the foil thing first, and skip the part about grounding it. Just don't skip the part about making sure it doesn't touch any of the other pins. Like was said -- it theoretically should still work as a shield as long as it completes a circuit around the tube.
And here's another tidbit -- you'd be better off making sure the foil was touching the tube everywhere but at the bottom, rather than leaving a little space. Why? Because it'll conduct the heat instead of trap it. Just make sure to give it a little flare at the bottom (yes, like bell-bottoms), so that it doesn't touch the pins.
If this makes you too nervous to do long term, at least try it once to see if it solves the problem.