I figured out how to do this using aggregate and history. Here is a working prototype.
To see its functionality, you need to create a classroom code and then open up that classroom in a bunch of different tabs simulating different students.
The one bug is that if students in the same group click the action button to find their role within a few seconds of each other, the aggregated list hasn’t updated yet, so those students will receive the same role. Not sure how I can get around this, but I’m open to suggestions.