Storage is cheap and text requires a minimal amount of it, so one easy solution is to store all submitted versions of a line, along with their associated user. Others can set a preference for what user's lines they'd like, and essentially give their own ranking to the translations. E.g. someone likes user1's translations and thinks user2's are ok, then he can set user1,user2 in that order and the system will display, for each line, submissions from user1, and if there aren't any, then user2's, and if there aren't any, then default to whoever else was the last to have submitted a translation for that line.
This will also solve any edit wars; if two translators disagree on how one line should be translated each user can choose and receive whose lines they prefer.