When playing games that are supposed to eliminate some of the players and then speed up, you can always play as teams.
In my group games with that kind of mechanic do not work, we are simply either too competitive or too strategic to come to an entertaining experience for everyone.
This lead us to play in teams so that if one 'player' loses there are always two people that can start playing something else to be entertained while the rest sort out what happens next.
You can play in teams in two ways.
The first way is a strict team. Two people per avatar army or whatever else represents a player in a game. In games that take a long time to play because of strategy or because of a dominance mechanic, this works out because it lessens the amount of players and it gives you a chance to collaborate and play in a style that you may not normally play.
In our group we have players that are volatile and risky and players that are very reserved. Usually when we make teams we put one reserved and one volatile together. It leads to very interesting game play.
The second way to play teams is to play a cooperative version of a game. That is to say each 'player' on a team gets his own avatar/army whatever represents a player in a game, and for all intents and purposes, they must win together.
This leads to very interesting play also because you must choose sometimes to forget about your own ambitions and do something to help your struggling teammate to get to a better place in the game.
We frequently play that this alliance is only skin deep however. When there is only one 'team' left (2 players), it becomes a rather quick game of 'back stab your brother' to see who ultimately wins.
This is my favorite kind of 'team' play because you are going to help your 'teammate' but only enough that once you two have eliminated the competition you can still compete with one another. It gives you a reason to play with another player but only enough motivation to keep them from losing, not outright ensure they prosper.
With this mechanic added to a game you need to add some simple rules:
As long as you and your team mate are not the only players in the game, you may not take actions against one another. That is to say you can't fight each other or otherwise do things that would detriment the other player unless the only action you can take is to do so.
If a single member of an opposing team is eliminated, the other member of the team is eliminated also.
I do admit that this leads to a fair amount of people who cede once they are on the remaining team, but that is OK because there is still a clear winner and everyone got to play together.
Your mileage may very but we have had lots of fun playing this way.