Are you willing to put columns on either side of the projector? If so, you could try running a single cross brace where you have blue lines, put columns on either side, then tie the cut end into that.

I had this same issue for a single point on a longer railing, so I used a toggle bolt. They have wings that are spring loaded and expand once they get past the wall board, then you can tighten as needed. They’re basically like trying to put a cat in a carrying crate. However, I only did this because it was one of many points on the railing. If the whole thing wobbles, I wouldn’t bet my life on it.