look at the cost of a fixed TV OLED size.
Now, look at your wall in your house where you want that TV to be placed.
Look at DIY solution with black or silver paint, not white and regardless of your projector you will find a much cheaper solution but your screen size will be much bigger and while you have ambient lights on, you will see your movie, shows just fine.
Some food for thought.
Here are some videos to see how they look. Paint cost also in this link.
Actively shows how this technology looks, even a 2.35 ratio in the basement.