I decided to make this a separate thread since it's more dominion related and people might be interested in the design concepts without a specific interest in Dungeon Crawl Stone Soup.
Both DCSS and Dominion are games that you can play solitaire, and it functions just fine for that. Dominion has a great way of combining the solitaire experiences to make things more interesting, even if there are no attack cards.
DCSS currently has no multiplayer functionality at all. They frequently mention tournaments, but if you look and find out how the "tournament was structured", it was largely a competition of who sat in front of a pc the longest to grind the most wins within two weeks.
The only easy way of adding interactivity I can think of would be to replicate the "strategy selection" phase of Dominion.
Two players go into a chatroom, where a script is running. The script repeatedly offers pairs of initial settings, along with monotheistic or duotheistic god restrictions.
Each player secretly messages the script which of those options it finds better. In the likely event they choose the same thing, the pair is thrown away and a new pair is generated, until the players disagree.
Once the players disagree, each player gets the settings he chose and gets a small finite number of attempts at a high rune count (I'm thinking 3). Only the best run counts, and whoever got the most runes wins (with some kind of tiebreaker).
The reason I don't think you should count the weak runs is that it would over-emphasize consistency. Consistency is already inherently emphasized, if you consistently get to Lair you have 3 times the chance to get a unique weapon in Lair that carries you to a high runecount win than if you didn't.
It would go something like:
Human Fighter who only worships Cherybdas or Xom OR Naga Venom Mage who only worships The Shining One