I've been watching the projector scene for a while.
Given your constraints of a deep room and cathedral ceilings ...
Have you considered a UST projector?


Until recently, I've been dismissing UST projectors for a few reasons as they used to be priced out of reach and had very limited screen sizes (120" max). But that's changing

Pricing is starting to drop below $3k (us) and there are a few which claim screen sizes of 150". I'm definitely starting to rethink my projection strategy as UST evolves.