The main website has a search by feature function which allows you to narrow down your selection significantly and include throw distance/screen size as an option.
Using 23 feet as the distance and a 360" width, this is the list of models that can do it.https://www.projectorcentral.com/projectors
Be aware that with a nearly 330+ square foot screen, you need 5,000 real world lumens, in a DARK room to get acceptable results. I would likely be looking at a projector that delivers 7,000-10,000 lumens for acceptable results.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.