I think you have a lot of compromises you have to make when you go with a front projection setup in that space. Keep in mind that this would only be available for after dark viewing and the placement location would make mounting the projector fairly difficult.
The W1070, with an 84" screen must have the lens between 7' and 9'2" from the screen (no more, no less) and the projector must be placed at about the bottom edge of the projected image, up to a few inches below if right side up, or must be placed even with the top of the screen to a few inches above the top if invert (ceiling) mounted.
If it were me, I would likely look into what it would take to change the built in so it would accommodate a much larger display. While it may be some work, and kind of messy, it would still likely allow for a 60"-70" display in the space rather easily. As it is, the opening looks like it could handle a modern 50"+ display if properly mounted.
Front projection is great, but it really has a 'place'. Family room setups can be interesting, but ambient light runs rampant, which means this would be for after hours viewing only, and would be rather high, while aesthetically impacting the space a fair bit.
While it is not my recommendation to go front projection in the space, it is your decision. There are some ways to get the most out of this type of setup, but all of them would still require some construction work to do well I would think.