Sorry, Capes. I wanted to keep it as simple and straightforward as possible. I knew it wouldn't fit everyone perfectly, but I don't think there's a structure that would. I could have let you pick more than one, but that would throw the numbers off. So, like I said, if you find yourself in more than one TZ, just pick one.
As for the polar regions, I was assuming they'd just keep UTC/GMT (since it's more or less arbitrary at that point), but it seems not. I just checked Wiki and found
this list of antarctic research stations. It lists time zones for several of them. Amusingly, the US station still observes daylight savings time...