Ahh...that is a tricky one.
A little bit more info about your screen might help narrow it down a bit. Is it 16:9? 2.35:1? Curved? Masked? Any gain?
Just going strictly by square footage, and assuming unity 1.0 gain, if you'd like to be somewhere in between 12 and 18 foot lamberts, you'll need a good 1800-2600 genuine lumens coming out of your projector. That number will go down a bit if you have any positive gain to your screen, or a curve.
Also, any plans to use an anamorphic lens in front of the projector? That can cut you light output by up to 20%.
And any plans for 3D? That can cut anywhere from 50-75%!
So you might need as much as a genuine 5000 or more lumens if you want bright 3D.
If around 2500 actual lumens will suffice, you'll want to look for a projector rated at 6000-8000 lumen output. Certainly, the normal 800 lumens most home theater projectors put out in calibrated mode will not be enough. And even in their "maximum brightness" modes, where colors are not as accurate and contrast and black levels suffer, they're still shy of 2000 lumens for the most part.
So you're definitely wanting to look into a different class of projector. Unfortunately, the prices tend to skyrocket above the $10,000 units, since the number of units sold above that price is so much smaller.
I'll have to look into some specific models, since I'm not intimately familiar with this price class and more of a cinema level projector. But hopefully we'll find a good option for you. I'm guessing it'll be DLP. Maybe 3-chip
