Not sure the feasibility of this, but seeing as we already get the numbers in the arenas while in the lobby, would it be possible to get the side splits as well? Maybe to keep the screen from getting cluttered you can Right-Click the arena you want to check, and get a "Side Splits" option?
It's a faint hope, but MAYBE if people coming in can see there's 50 Bish, 100 Nits and 80 Rooks in LWB, but 100 Bish, 70 Nits and 40 Rooks in LWO it might encourage them to pick an arena that would help balance sides (say, a guy who normally flies Rooks sees his side is fairly up in numbers in Blue, so goes to Orange instead).