Ok, so this is my first post, and I have no idea how programmable this idea is but I had an idea for a mode that would go faster than sequential but be a little more fair than freestyle (for those that can't hit refresh all day waiting for their turn to gain that slight advantage):
This is the rough idea: It would be like freestyle, everyone could play whenever they wanted... BUT, armies would be 'awarded' to each player every time a player took a turn. The armies might be awarded as V/N, where N is the number of players and V is the number of armies that a player would earn if they took their turn right then. They would be added into a pool which the player would get to place when they took their turn. This would just be V if they maintained the same territory and every other player had gone once. Fractions could be carried over for the next turn.
In other words, each time a player went, everone would earn the appropriate fraction of their armies to be distributed later.
For example, say I own 15 territories (no continents in this example) at the start of my turn, and we are playing with 5 players (n=5). After I finish playing my turn V=(15/3) and so I would recieve 5/5 or 1 armies into my 'pool'.
If the next guy took his turn and took 3 of my territories (down to 4/5), then I would get 0.8 more that turn. Another guy takes another 3 of my territories and its down to 0.6. Say I decided I'd better hurry and take my turn now before more was taken... well, then my current total is 2.4 armies... so I get 2 armies, and the 0.4 gets carried over.
But if everyone goes twice between my turns then I get those armies added up over all those extra turns... except now I have to wait until everybody goes again next turn to get a full set of armies.
So you would have to balance the benefits of taking your turn sooner with waiting until later...
I know its probably too complicated and involves recording fractional armies, but I was trying to think of a way to make a game as fair as sequential but faster.