Realistically, you run into issues because of the screen size. Unfortunately, there is a huge gap between the 'typical' home theater projector (under 2,500 lumens) and the brighter home theater models (4,000+ lumens) with full 3D support.
I would most strongly recommend the Digital Projection dVision XB-35-1080p-3D model which delivers a full 1080p 3D image with 4,500 lumens in one of the most silent running operations available. So, you not only get the brightness you need, but you don't end up with a noisy projector in the space.
Unfortunately, that runs a bit over $20,000 without a lens. Another $1,000-$2,500 or so depending on the lens needed.
Here is the list of projectors under $15,000, sorted by brightness (not cost) that are 1080p full 3D models currently available:
Find Projectors By Feature
Pretty amazing to see that four of the top five listed are less than $3,000 and the top one is barely any brighter at over five times the price.
This is the non-3D version of what I would recommend:
Digital Projection Projectors: Digital Projection dVision 30 1080p XB DLP projector
Using the projection calculator you can see that you get plenty of brightness on screen with a 220" diagonal...
Digital Projection dVision 30 1080p XB Projection Calculator - Throw Distance and Screen Size
With a minimal gain screen you get more light than needed, but enough to truly create an amazing image in either 2D or 3D modes.
By comparison, the Epson, simply can't deliver anywhere near that size or quality:
Epson PowerLite Home Cinema 5010e Projection Calculator - Throw Distance and Screen Size
I wish there was something of the Digital Projection quality which had the brightness that you needed at a more Epson like price... But, they just aren't out there yet.
