Do you think having all the members of the subreddit (or the entire site) vote on who the mod should be? I think there are many ways to make this efficient by statistical sampling, proxy votes, and detecting when statistical errors occur. To restrict people to one account you'd need to verify phone numbers.
I'm currently trying to build this but I'm not a programmer so it's slow going. I'm interested in your thoughts as I'm sure I'm missing something obvious.