You can go with something like this which will deliver a native scope image to your screen and save you from having to buy a anamorphic lens and sled setup which would be extra cash running a fair bit...
Not really close to your budget unfortunately.
At the end of the day, you want something which delivers about 1,600 post calibrated lumens on screen, which is not as bright as it used to be. This is based upon a screen which is 66 square feet in 16:9 mode, and about 74 square feet in 2.35 mode. With 18 lumens on screen and a 33% loss of light due to the screen perforations it gives you some leeway.
The hard part is that for exceptional color and contrast you could very well be under budget, but if you are willing to give up just a bit, you actually have quite a few choices available well within your budget.
Overall, these tend to be lesser expensive options, but may give you something you just want to 'try out' which comes in at a far lower price point. No, these won't look as good as some of the higher end models, but
It is worth noting that companies like Digital Projection, which have a huge booth at CEDIA, really don't distinguish their dVision 35 series between business and home theater use. They look amazing in both settings and the same setup is used at Infocomm and CEDIA (business/residential). But, they are pricey. I'm a fan of the dVision 30-1080p-XC which is a 2,900 lumen model with good contrast. Closer to $18,000 or so with a lens it may be out of your price range and this is not a 3 chip DLP model.
Projection Design also has their M-Vision series which come in a fair bit less than the dVision series and you can get their high contrast version for under $10,000 with a lens.
Where you want to go with your setup is up to you as much as anything else.