It's a good point, but PEX is installed above the sub-floor to circulate the heat and then the mud floor for the tile is installed on top of it. It shouldn't add any height, since the mud floor already has to be 1" to 1-1/2" thick.

I will be adding an access panel so I can reach the damper that will be suppling that duct. We don't want air going up that duct into the daughters room, it has 2 ducts because the homebuilder messed up and ran the duct up the wall that was meant for the master bedroom but was to far over and ended up in the side bedroom and they just decided to leave it because home builders are idiots. I am thinknig about now adding a T to the duct and having 2 supply registers to even out the airflow a little bit

I find the current arrangement of dense shelves around the TV sort of overwhelming, which would only be made moreso by expanding them both vertically and horizontally. Do you need all that storage/display? I think I'd prefer a long console under the TV and then maybe a single storage piece in the corner or elsewhere in the room. You could have some art instead of all that visual clutter.

You can get custom vent covers water jet cut out of your stone or tile. Here is one company that does it https://stonecenterinc.com/heat-register-covers/ Is there any way to move or eliminate that particular vent, given that there are vents to each side? Usually if I am designing something that is a feature, I try to relocate anything that I feel interrupts the design. Particularly if you are doing a minimalist style design, the solutions for minimizing the impact of vents and outlets and other necessary utilities can get awfully expensive., and the cost of just moving it (if possible) may intersect with the esthetic or decorative solution.