This is really interesting! I'm not sure there's an organic solve here, but let me try! Right now, think there are two ways that I might handle this.
1. Have the chaser (the ghost, I assume) @ tag the investigation into each room, chasing them through the house. This is a bit like where the ghost chases someone downstairs, somewhere much worse from where they started.
2. The chaser and the chased both talk in the walkie-talkies channel, while everyone else is muted. The trick here is to keep it short. We do break some rules in the game (ghosts talking) but I think this is a fun highlight to do once a session?
But I'm not sure, like I mentioned, there are a lot of technical constraints for this game! I'd be curious to hear how others might handle this.