I won't assert that the flow cannot be maintained without the flip, but I will say that there is very little material in the Dooku scene to begin with. It's already cut very closely, so to say, so there's a very limited number of things that can be done with the shots.

Dooku flipping down is a crucial moment in the pacing of the scene, but it doesn't have to be the flip. It just needs to be SOMEthing of Dooku, but it simply doesn't exist.
(I recently had the idea to film a guy in a Dooku costume stepping down the stairs from the knees-down, which would accomplish the same thing in a more down-to-earth way, but would be way more work than it's worth.)