If UCF, Cinn, and WV really want another east coast school (UConn) then they need just one more vote to make it happen. It takes 75%, 9 of the 12 members, to add a new school. So those eastern three just need one more to block any additional members unless UConn is one of them. One they could approach is BYU. In turn they could agree not to support Utah (would BYU want Utah in the Big12?).
Maybe they would not want to do that since two of them are new and all are just happy to be there. But if this round of Big12 expansion is only western schools, that wouldn't be ideal for them.