Moving water defiantly pushes living creatures. Go into adventure mode. Jump into a river near the edge of a waterfall(the shallower water shouldn't push you off right away) and try to go upstream.
You will discover that it is very difficult to because once the water gets to a certain depth it pushes you back toward the edge. And you KNOW you aren't telling the adventurer to go that way.
I believe that anything 4-6 will push when it moves and it is "flowing". Anything below that is too shallow to move you(I have a hypothesis that 2 and 3 depth may be able to push smaller creatures) and 7/7 doesn't actually move unless there is a shallower tile near it. It just knows weather it's stable(no flow) or flowing. (waterwheels work but doesn't actually push. It just knows that the water is terminating somewhere along the line.)
If the water is the right depth but isn't "flowing" (a partially dried murky pool for example) the game knows that the water isn't actually going anywhere so it doesn't have the force to push you.
Most of this is just guesswork at what the code looks like but I have done the waterfall test myself by accident while hippo hunting. And water DOES push. Just not if you throw out a crazy amount at once. The pressure thing with the opening at the lowest floor most likely will not work. as its teleporting the water to 7/7 immediatly, not flowing it. Only once it gets a few spaces away from the tower will it push. And probably only 1 or 2 tiles.