I've played a few of the GOTMs over at Civilization Fanatics, and it really does enhance one's enjoyment of the game. In fact I've even run a couple of Civ GOTMs at my guild's website (but I have no interest in doing that here, as I'm too busy these days). For me it doesn't really matter how scoring is handled; I just like playing the same scenario as other people and seeing how I did in comparison. Even so, some objective yardstick can be useful, if only to see how different people play the game.
I'd suggest multiple "prizes" for each game, in a lot of different areas, using the game's stats function. These might include not just score (heck, I'd still be curious how high scores can get), but also things like most starships constructed; most total ships constructed; quickest time to victory; quickest time to defeat (!); highest winning AI Progress; lowest winning AI Progress; most worlds conquered; fewest worlds conquered in a victory; score after five hours; a prize for playing the scenario for 24 hours of in-game time; etc.
At Civ Fanatics, the mods also regulate when people can start posting AARs and screenshots. After a week, you can post pics of your first five hours, something like that.
As for difficulty, I think it's a good idea to make the first couple games in the 7/7 range, but if the idea takes hold, have some games that are tougher, just to push some of us out of our comfort zones. Like me! Also, ideally the poster should playtest the GOTM before posting it. Maybe not all the way to victory/defeat, but at least long enough to scout the whole map, or some such, and ensure that the game is a reasonable and interesting challenge. I don't remember -- is there an editor that would let someone create a custom map or scenario, like the tutorial campaign? That could be especially interesting, if it were well-tested.
Anyway, it's a great idea, and I'd be interesting in playing a GOTM.