I experimented a bit, but didn't find any solutions. The issue I was facing is how to manage which unit attempts to go through the pathway first so that units don't compete with each other.
This would require more work to figure out than I'm willing to invest, since it basically means designing a way to store where each unit is, and how to process all of it so that they work with each other to get through.
One thing that comes to mind is using a dijkstra map instead of pathfinding, since that creates data that multiple units can use to move through a level. That way, each unit would have their own way of finding a path to the destination without generating one for each unit.
edit: also with a dijkstra map, the units would be moving towards the next tile rather than being pulled by something that could be currently behind a wall, so the flow of forces would be more accurate. You could also stop other units from trying to get to a tile if that tile is already occupied by another unit.