Here's a test of the idea. I used a higher resolution tilemap to make the water motion jump in smaller steps. I also made it so cells can have higher priority so it fills falling the shape of the corridor more or less.
dropbox.com/scl/fi/g9pu4fcr9qdkmo7weqjbw/flooding_idea.capx
Again you probably could make the motion smoother by gradually moving the flood sprites from one spot to another and running the flood function once they stop at the destination.
One thing I'm not super happy with is we have to call the function from separate events instead of under a repeat condition. That's do to a quirk with picking and newly created objects.
A smoother and more complex idea still could be to trace the polyline that makes up the corridor and then starting with the point where the water starts from move two points to the left and right along the polyline. That would basically give us a fill line. Probably could come up with some kind of logic to decide how far each edge point should move to add a certain amount of water per frame. I'd imagine you could borrow some ideas from a triangulation algorithm like "ear clipping." Anyways, that's just a general idea, I'd imagine it may end up being simpler to do than you think but I'm not sure.