Unfortunately, to my knowledge, you aren't going to get it.
The BenQ HT2150ST is a short throw model which will be better than the Optoma and has a bit of zoom, but isn't anywhere near the Sony in image quality. It has no lens shift, and must be placed at the top edge of the screen.
It won't reach the black levels of the Sony, or the quietness of the Sony.
Sony has a ultra short throw projector, and it's $25,000:http://www.sony.com/electronics/projector/vpl-vz1000es
I'm sure it is excellent.
The reality is that good short throw is hard to achieve, and the lensing system is tough to get right. Ultra short throw is almost always a terrible experience. While we have seen an uptick with a few short throw models, like the Optoma and BenQ, they aren't top shelf units. They are entry level.
Because the lens trades off some image quality for the short throw distance. The ability to add lens shift would be well outside what short throw is capable of. Likewise, even getting a bit of zoom is unusual. So, when manufacturers are asked to deliver the best quality, for the lowest cost, they don't make short throw projectors. They make standard throw models, like that Sony you had. Or the Epson 5040, or the JVC models. The cheapest projectors are almost always mid-throw projectors as well. The lenses are cheaper, and the quality is better, so that's what they make.
This leaves people who have your type of setup really in a tough bind. You fall into a room which isn't standard for front projection, and your budget is almost meaningless because people that have $4,000 to spend, have rooms which support a nicer projector, which manufacturers agree upon will not be short throw.
I'm sorry to say that you aren't going to find anything that I'm aware of which will touch the Sony for anywhere near the budget you have, and only the Sony 4K, linked above, is comparable to the Sony you returned.
Something like this might work, but is probably in the $15,000 range...http://www.projectorcentral.com/Digital_Projection-iVision_50_1080p_XL-projection-calculator-pro.htm?td_=6&id_=100&l_=1787
I know, it sucks.
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