A cheap LED model like an LG PA70G/PA75G will do that size screen with light control. Cheap cost, no bulb to worry about, no real care and feeding of the projector (i.e. you buddies can turn it off then right back on without consequences).
It's DLP, but the equivalent color wheel speed is "high" from what I hear. I could see rainbows on slower color wheel speed DLPs (like the first 720P RP DLPs that were maybe 1-2x), but past that I can maybe catch a glimpse, but it's not even remotely distrasting. I never see them on my LG projector, and I've even tried looking for them.
IMO, RBE is completely blown out of proportion as an issue with single chip DLPs. I find image quality issues like high black levels and lack of contrast at high or low IRE much more distracting personally. Even when you see a rainbow, it's typically on a very high contrast edge moving quickly and it's just a fleeting thing. But like I said, a very small percentage of people can see them on modern projectors with their higher colorwheel speeds or LED cycling times.
Give the LED projectors a thought, as they are more robust and cheaper to run than a bulb projector of the same approximate cost.