If this is your model, would you mind making the first pic a picture of it installed? It's hard for me to visualize how it is supposed to work.
I looked at doing this exact thing and on my blinds there’s plenty of room in the top construction of the blinds to put a servo in there you would never see unless you’re looking for it. The rod itself was even not perfectly round so you could 3d print a shape to go around it very easily. I’m honestly shocked there’s not an aftermarket company already doing this exact thing.