Ok so 3v3. If a challenger is facing the gym, he cannot do anything else in the league until he's fought us both. And if he loses to one, he has to start all over? So like... consecutive wins against us is the only way to get the badge.
As for the teams, we should each get a regi as a signature poke, and then two other fossils/ruin pokes? And we can always change the other two pokemon, but the regi will always be in the team.