Twice now, I have hads either built-ins or custom build furniture that gave my RPTV a nice, hidden, built in kind of look. Both times, I have had false doors over the bottom portion of the TV so that only the screen was visible. In my opinion, that give it a very nice look. Since I have always had a 5.1 system set up, I never use the TV speakers anyway. Also, even though the controls were covered up, the remotes have always worked. Here are some random thoughts.
1. When I bought my Marantz RPTV, the support folks had a whole document about how to convert it so it could be built in. This including removing the wheels and performing some other modification to the exterior. So, maybe Mits have a similar document. In my case, I did not use the documents because I did not need the screen exactly flush with the woodwork. I access the TV from the front, removing the false doors and wheeling the TV out of the enclosure.
2. When the RPTV is inclosed, heat can become an issue. Make sure you allow for proper ventilation. Since you have a whole closet, this probably won't be an issue.
3. The chamber for the TV can become a nice echo box (from the RPTV fans) if the fit is tight and no sound absorbing material is installed.
Since you have a whole closet, this probably wont be an issue.
Anyway, I would just go with a screen only visbile setup if your framing will allow it.
Regards,
Hal