I think this is an excellent idea. If a staff member is obviously the most active on Discord that month, bias from a minority of players isn't going to sway the vote. You mentioned that a kit mod isn't going to be as well known as an olympus mod, which is true, but staff don't only deal with their own server, and now that the bans website is back up anyone who's interested can see which staff members are muting more than others.
However I don't think staff should be taken out of the voting decision. They see angles of staffing that us players don't see. Maybe there could be two awards, a player vote and a staff vote (although 6 SOTM winners would be excessive) or maybe the two results could just be compared.
As I said, a staff member being more popular on a server, or unpopular with a small group of people, isn't going to override the "real winner." And I really don't think it's a big deal- its just a monthly award, and the only reason we should feel really cautious is if there's spamming in the ballots.
There will always be bias in democracy. That's why everyone gets one vote. We just have to trust that the results will ring true. And if a staff member is disliked by everyone, maybe - in a position designed to improve the server and help players - that's something that should be looked at.