Why don't you just have a pool/list of people who got voted in, scratch them off as they get voted in each week, and randomly select a few people out of that list each time you need to do a vote call? This way you can still have fresh contenders without having to be unfair.
Additionally, you can just enforce the fact people should be on around 7PM and can stay the duration, for people like me who always get called away or whatever when the time arises, you can just check the backup list you made earlier.
Also seriously, Skullgirls stream chats are the most unintelligent thing I've seen in a while, and I don't mean because people are dumb. People are smart but they copypasta shit all the time and drown out anything that pertains to the chat. Skullgirls hivemind is strong and unless you turn on slow mode or ban the people who keep copypasting it's just going to keep happening. I find it funny in short bursts but when I want to actually talk about a match and I see a flood of RAISE UR WAZPS im just gonna close the tab because (1.) you're going to be talking to chat and I don't care about chat (2.) if I have to divert my attention to anything other than the match im just gonna put it on mute or leave.
But yeah, make a google docs signup sheet or something, and pass it to all the people who want to run Who Y'all Like, make them put in their steam addresses, nicks, whatever, and then have a private, uneditable sheet for people who you want to queue up for WYL. Mad easy