I was thinking about a short throw projector for that room as well. They're not cost competitive with 85" flatscreens (particularly when you add a light rejecting screen), but there's something to be said about a huge screen.

https://www.benq.com/en-us/knowledge-center/knowledge/light-resistant-screens.html

Author of "Status 101: How To Keep Up In A World That Keeps Score While Buying Into Buying Less"