A few responses:
>There is nothing special about Gamecenter that would cause excess drain.<
As I stated, I ONLY get battyery drain when Gamecenter or a connected game is activated. This says clearly that Gamecenter is special. It appears that this app maintains a constant internet connection that requires power.
>No, this is not a telltale sign. The WiFi is always connected (or instantly connected) when the Home Button is pressed on all the iPODs I have tested.<
On my iPod, when Gamecenter has not been activated, the WiFi icon comes on 1-2 seconds after the Home button is pushed. Once Gamecenter is on, the icon shows instantly when the home button is pushed. Again, a difference is clear and repeatable.
>If you update to iOS 4.2.1, you may have success.<
It is true I may have success with this update, OR I may end up with an iPod that never turns off its WiFi connection and continues to drain the battery regardless of how many times I reset it. Any experimental result must be taken with a grain of salt until it is clearly replicated by other experimenters. At this point, I'm not seeing others having the same success you describe.