One of the easiest ways to make the "black" areas of the projection where you don't have content to fade away is to increase the amount of ambient light.
In a completely dark environment, it will always be difficult if not impossible to remove 100% of the black rectangle emitted from the projector. One technique we sometimes use is to add some basic up-lighting to the areas that you do not want to see the rectangle or increase the ambient lighting a bit.
Also, you can try reducing the brightness on the projector, playing with the contrast settings, and change the image mode — Cinema or Natural will be the best.
Another more advanced option is to wrap the lens with foil, (preferably black cinefoil, here is an example). Foil won't get rid of the contrast areas but will let you feather and shape the edges of the contrast areas to make it fade away. We have a bit more info about some related concepts here.