Build one box to test it out, put it around one speaker, and leave the other as is, no box. Switch between the two while playing music and movies. If you can tell a difference in sound, go back to the drawing board. If not, you're good to go.
Basically, putting a speaker in a box in never a real good idea. I couldn't tell you the exact science, but what I do know for certain is that every time I've help someone move their center channel out from under their TV in a little shelf in their entertainment center, it's sounded much different (for the better). Someone more knowledgeable than me should fill in the why (Something about radiating sound and a baffle, I think).
I'm not sure what kind of speakers you have, but it looks like they were designed to be wall mounted, which is good.
A better idea would be making a box frame, and constructing all the sides out of speaker fabric, or with as high as your speakers are mounted, a false soffit around your room.
There's also the idea of just painting your speakers to match your walls.
BTW, If there's any way to lower your speakers closer to ear level, you'll be much happier with the directionality of the sound matching what you see on your TV. Placing them equal distance from each of the sidewalls would also help, maybe even mounting them on the side walls. But yes, with the doorway where it is, and as narrow as the room is, I can see where speaker placement in your space will have to involve some compromises. Stands would be ideal, but it sounds like that's exactly what you're trying to avoid.