I think ELO would be perfect. It can be abused, but only to a limited extent. To achieve very high rankings only by cheating, one player would have to create many different accounts, separate them in groups, each group building one account to moderately-high levels, and then using those accounts to build only one of them. It could be an enormous effort.
If the accounts had some public history, showing all the games that was played, who else was on that games and how many ticks (and real time spent, for turn-based games) it would be somewhat easy to spot cheaters.
A good way to adapt ELO for multiplayer is to count the points separately against each opponent and summing at the end. You could consider a win if one player finished “above” another, so the Winner won against all other players, the 2nd won against the 3rd and lower but lost to the Winner, and so on. It would problably be fair to give a bonus to the winner, like multiplying the points of all pair-calculations that (s)he is involved by X%.
This would also change the dynamics of the games, for good and for worse. For example, people could think twice before quitting; The 2nd placed, seeing there will be little chance for win, could offer his/her services to the 1st place in order to maintain his/her position; The 3rd placed could also offer his services to the 1st place so (s)he can pass the 2nd placed; And all players would be interested in placing the highest ranking player below them, so they would gain more points.