@ATC, whichever one you you choose, I think we should definitely have a 1v1 on a Classic map on webDip, since webDip is focused on being the best in Classic Diplomacy.
When I first joined this site, I didn't have the patience to join standard games, and I found it difficult to find a live game that actually filled up and then also didn't NMR on the first move. Had there been a 1v1 on a Classic map, I think I would have played that, and then after getting a game or two of those going, I would have likely then had the patience to join some standard games.
1v1 seems like a great way for players to get a game going quickly, which should help keep new players interested. Plus, even though 1v1 is very different from 7v7, new players with no experience can at least get familiarity with the movement around the Classic map.
If you add two 1v1 variants, I think the one that @Captainmeme suggested looks interesting and balanced:
"The one I'd recommend is Duo (http://www.vdiplomacy.com/variants.php?variantID=22), perfectly symmetrical yet has an incredible amount of strategy involved."