I think eligibility should be based on a minimum karma-within-subreddit (comments and submissions) threshold.
And yeah, this would cost Reddit some in admin labor, but they should be able to use some of this revenue stream towards those few hires. I'd imagine a team of 6 would be plenty for this purpose, maybe could get away with 2 or 3.
Voting? Who has the right to vote? Anyone? Any socketpuppet account? Only verified real people? (would be a different reddit)
The base problem is called politics.