The bracket fits, I have the same one and also had the same projector (TH683), which was great by the way, but I had a hard time changing it because it had a great black level with 1.3 lumens.
Nevertheless, I bought the Benq X3000i. The black level of 1.55 lumens is slightly brighter than the TH683, but with the higher resolution, the X3000i makes a great picture. I often play games that are very dark and the details are very easy to see. I always wanted a projector with a great black level, but then you have to spend a lot of money. The Benq X3000i is highly recommended in all areas, including black level. Kind regards Urs

Unfortunately, I cannot tell you whether your bracket fits the projector. It has 3 mounting holes. You can find the exact dimensions on the BenQ page.
I am personally very satisfied with the colour space and black level. But there are different opinions. I would definitely buy the projector again.