With a 3000 lumen requirement, it would be difficult to find a 1080p full HD projector displaying that much lumens...
I know this would be similar to getting what you already have, but you may consider it in order to not sacrifice the lumen output.
MX812ST has 3500 lumens, 4600:1 contrast ratio, 3D ready, 2 10 watt speakers, 1024x768 native and 1600x1200 at maximum. The main strength about short throw projectors, which is why I'm recommending this unit, is that it will bring more than the listed lumens to the screen due to the fact its projecting the image at a shorter distance. Ideally this will help with your lighting control issues.
If you however want to move away from the 4:3 display and move towards full 1080p you can check out the W6000 which offers 2500 lumens (less than your request of 3000, however is very bright), 50,000:1 contrast ratio, 1920x1080 native. The W6000 can be had as a refurb unit at around 1.5k, while a brand new one will run at about 2k.
I Love Apple, BenQ, Samsung, and Acer Products = )