If we raise difficulty levels, then we will never get any new players. There are still people new to Civ3 showing up here occasionally, and if we have lower-level games we may be able to get some of them to play, especially if we advertised it ahead of time. My kids are willing to give regent and lower level games a try (warlord is their current comfort zone), but they won't even look at monarch and above, even with great starts. (I mention this because we are averaging about 8 submissions, so an increase of 2 isn't insignificant.)
Looking back over the last 14 games, there are four with at least 10 players - at Regent, Emperor, Demigod, and Sid (very easy game). There are four with 6 or fewer players - at Monarch, Monarch, Emperor, and Deity (very hard game). The level of the game does not seem to have much affect on the number of players.
We might play more games on smaller maps. Tiny and small maps play a lot faster than standard maps, though the research rate messes with 20k games in a way I don't appreciate but no-one else will care about. In the last 14 games, we've played one large map (a regent game with 9 submissions) and 13 standard maps.
I'd like us to continue playing at all levels and try to drum up some business among current non-players. At lower levels, we might suggest optional twists to the game to make it more interesting to better players. I don't really think mandatory victory conditions are the way to go for COTM, but optional additional conditions might be interesting. For example, one might try for conquest in a warlord-level pangaea game, but only allow attacking when your empire has access (through trade or natively) to all 8 luxes, or play a low-level tiny map for 60k with no temples allowed.