What if a press held a contest, and everyone who entered the contest got to vote on the manuscripts the press received? The manuscript with the most votes is the one that gets published. Only entrants get to vote, so the entrants themselves are the judges, but no one can vote for their own manuscript.
Would that work?
UPDATE: I'm not as creative as I thought. It looks like this idea is kind of already being done, as reported here in Poets & Writers magazine.