If the stalemate continues, both players come to a mutual understanding that the game will not continue until a player detonates Roots of Yggdrasil In other words, both players will continue to draw 2 cards every turn until Roots of Yggdrasil activates
Even if you pull Baba's Gengar, he will say "Genga!", So you will be able to tell who has Baba
You can activate one of Grist, the Plague Swarm's loyalty abilities the turn it enters the battlefield
However, you can play a few as late-game options
Enchantment - Class Central Elevator When you unlock this door, search your library for a Room card that doesn't have the same name as a Room you control, reveal it, put it into your hand, then shuffle