So it is a 12' wide by 9' high projected image? What is the screen surface? What are the lighting conditions? Do you have a set throw distance requirement? Are you going to be able to put the projector where it needs to be or might lens shift and/or keystone correction be required? Does the $1,000 budget need to include the projector mount, hardware, cabling, installation, etc.?
There are a number of projectors that meet your 2,200-3,000 lumen and $1,000 criteria but if yours is a typical situation then that is likely not a recommended solution. For a 9'x12' image you would need an almost cinema like environment in regards to light control in order for a 2,200 lumen projector to be recommended. In a more typical presentation space I would probably consider at least 3,500 lumens or so and probably something more around 5,000 to 6,000 lumens.
