It's an interesting idea. It would count as a new flashpoint though, not as a reinterpretation/upgrade of existing ones (which, personally, would interest me more).
Well, they could take elements from my suggestion to "spice up" current flashpoints by adding different objectives and outcomes to the existing scenarios.
For instance...take the Esseles run. It currently has two different distinct flavors (Rep and Imp) and also two different directions on the Imp side depending on whether or not you kill the captain. Let me start here and break down some spots where they could insert secondary goals or even story arcs.
Current (make it to bridge) or bridge destroyed/escape scenario. Either one would be randomly determined when the door is blown open in the cinematic...determined by which elevator you can use. The escape scenario would have you getting to the shuttlebay before the ship is destroyed, saving the ambassador, passengers and crew along the way.
Your goals are to open doors by restoring power, fight off boarders, prevent core meltdowns, etc. Even using automated gun defense system to disable the tractor on the enemy ship so you can escape in a shuttle.
At the shuttle you can choose to escape or try and save the ship by boarding the enemy ship.
Once there you can choose to either disable the tractor (current quest line in place) or try and take the ship by force.
This way you have multiple outcomes and branches, and most flashpoints and heroics could be changed in this way to add variety based on your choices.