A good quality picture comes from a dark room with front projection. Unlike your rear projection unit which has a sealed projection light path, front projection does not. So, you are going to need as dark of a room as possible at all times for viewing. The reward for doing this is a stunning image which typically rivals the local movie theater experience.
Looking at the room, I'm not sure what to do. The pieces on the side are not ideal, and really interfere with everything, significantly IMO. I would be looking at a good tab-tensioned motorized screen, or some other solution to get a screen size which is a (fair bit) larger. About 120" or so would be where I'd start looking. Maybe as much as a 133" or even larger. Going to nearly twice the diagonal (4 times the size!) of your Mits. is a completely different experience.
The JVC is not spectacularly bright, but delivers the best 2D image available under $3,000.
The Sony is a new, and very nice model, which is priced a bit better, and is brighter, but doesn't have the same contrast (nearly) that the JVC does. Still, it may open your budget up more for some screen options, or other options.
I really like the room, and visually like the built-in units, but hate how it impacts the potential setup. I just want them gone.