Not knowing your initial layout, and seeing that you have ceiling height at 8 feet, I'd consider sheetrock on the ceiling, and running soffits on the sides of rooms.
For the junction box, you have few options:
1) Leave a little cutout in the drywall (3x3 in or 4x4 in) below the box, where the box can be accessed. You can use a custom cut piece of ceiling tile with brackets to hold it.
2) Re-work the electricity so that a box no longer exists - least preferred route.
3) Lower the box so that it is part of the drywall. Put a blank wall-plate over it.
You can always tile the ceiling per earlier post, I'm just not sure how low it needs to be from the ceiling studs. In my basement I went full sheetrock in the ceiling with soffits. All HVAC, electrical, plumbing are in the soffits. I do have a few cutouts where I needed water or gas valve access.
Get a bunch of opinions, check codes.