Thank you very much for the kind feedback, Daniel P.,
This looks like an interesting project. My interest in those projections and panoramas is surely motivated by one of my Professors back at the Univerity of the Arts, Berlin, to get my MFA. Since I had studied Architecture before, as he had, we had long conversations. I learned a lot from him. In this way, I'm always happy to pay forward.
https://www.asisi.de/en/yadegar-asisi/biography
Here is one example of how to map the texture and adjust the geometry of the Dome. Then, use a camera setting that resamples the Projector specifics, including position/orientation.
https://www.youtube.com/watch?v=z_DyFhhYiL8
I have more of those little snippets on my YouTube channel.
My best wishes for your project, and please if you have a minute, after the project, can you share a link or an image? Thank you!