I have an alternative suggestion that might fix the problem. It comes from competitive Diplomacy (the board game), and it’s the best draft system I’ve ever seen.
At the start of Draft, every player secretly selects their top-5 character choices. No one gets to see the other player’s picks. Then have each team ban two characters. If one of your choices was banned, it’s eliminated from the list and everything moves up to close in holes. Then, people with banned picks can fill in the bottom of the list. Once everyone has 5 picks, the computer goes down the list from top to bottom. If you are the only person who picked a BB at slot 1, you get that BB. If there’s a tie, the computer randomly selects who gets the pick. Once all first choices have been resolved, anyone left goes through the same process for their number 2 choice, and it repeats until all players have a BB. In order to keep uniqueness, you’d have the computer combine both teams for resolving the draft.
Since everyone picks at the same time, there’s no advantage to team order. Since you pick BEFORE the bans, there’s no advantage to having the first pick after the first ban. It also encourages both diversity and meta, since you can’t see what the other team is loading, and you’ve always got a mathematical chance to get your favourite choice.
In Diplomacy tournaments, it’s almost unheard of to get anything lower than your third pick, and there are only seven choices. With 30 BB to choose from, I would expect the same outcome (once you factor in the bans).