The earth is what's goin on there
You see, the earth emits magnetic fields (thus the reason for Santa at the North Pole
)
And these fields affect your monitor, as well as other possible magnetized things such as various metal that may be around it in your cabinet/etc.
In any case, I'm betting you are turning it on, then tipping it on it's back while it's on.
Do this instead: Turn it off and leave it off at least 20 minutes. Turn it on its' back and turn it back on. The screen should look much better now.
The reason this happens is that when you first turn it on, it demagnetizes the screen (the thud you hear on computer monitors, and a quieter sound on most TV's). This removes any effects of earth magnetism on the screen. However when you tilt it (or even twist it while flat), the earth affects it differently and discolors the screen by affecting the metal shadow mask in the front of the screen.
You need to turn it off at least 20 minutes for the demagnetizing (Degaussing) circuit to reset, since it generates a lot of heat in a wire surrounding the tube, it can't be used until it cools itself of.
Note: If you move your cocktail table once it's installed and upside down, you will again see problems so put the game where you permanently want it, then turn it off, wait, then back on and things should be fine.
Worst case, you may need to rent/buy/build an external deguassing device, but I doubt it.
Also watch out for unshielded speakers--a degausser won't help that, you need specially shielded speakers to prevent monitor discoloration/damage.