Pretty sure your concept is flawed from the start.
It might sound nice as a 'what-if' scenario, but as soon as you get into any of the details, it falls apart and hopefully shows us why games and stories are typically focused on the people doing something.
Now, if you want something a bit more likely to succeed, you can make a "Damsel in Distress Simulator." From the get-go, you can start to think of gameplay mechanics like combing your hair, talking with guards, taking care of birds, etc etc. The ideas just flow, instead of trying to fit a square peg into a round hole.
In fact, this could loop around to your idea of helping the rescuers by opening up opportunities for the princess to sabotage her captors. You can have a Majora's Mask-like timer which keeps track of how far the knight is from saving you.
In the original version of Oblivion, they run like they do in Morrowind.
It was until Skyrim that Bethesda properly implemented partially turning the character when running sideways or diagonally.