I think as I build on the narrative in the future, I'd like to add more options and branches to the narrative as you suggest. I originally had a few simple interactions in the memory scenes, but I felt that they distracted from the story and therefore felt a little out of place, but if I can build up the world to offer more interaction then maybe they'll feel a little more at home.
I took inspiration from The Book of Distance which I played a few years ago (I'd highly recommend it if you haven't tried it). In that, there are subtle interactions to trigger the narrative to continue which really helps bed you in more.
As a note, the slight consequence of which order you choose the objects means that the final object you select will have its own unique audio. But currently, that is all.