This sounds a little like the AC formula. In those games, I don't really feel like I'm in the animus, so I think direct control over the hero should be thrown out, otherwise the bits where you're not controlling the hero will feel out of place.
Inscryption is a very different game and I certainly felt more trapped, especially in the first third of the game. In that one, there's an ever present reminder that you're trapped, and there's interesting stuff to so outside the main gameplay loop.
So you need to play as the princess and make interaction with things other than the hero fun, but not so fun that you don't want to be rescued. I think you also need some kind of peril to give urgency as well. Some ideas:
- elements from Prey - hide from your captor when helping your hero
- puzzles and whatnot in your prison
- periodic checkins - i.e. need to be in certain places at certain world times
- limited control over your hero