There's one set of Theater View settings per library. As long as you use the bedroom PC as a client, they will share the same theater view config.
You could run the bedroom PC as a separate library and import the media files from the server. The media files would stay in one place, but you would have to maintain two libraries, so not what you want.
The way would be to make the File Info panel template definitions aware of the actual screen resolution. I'm not aware of any way to do that. You can present different file info panels depending on context and other factors, but resolution is not among them. Perhaps global variables could be used, but I've never heard of it. Exposing the screen resolution so that it could be accessed by an Expression (which could be integrated in the File Info Panel) is a feature JRiver would have to add.
The only other thing I can think of is that if you playback to a different ZONE only when using your bedroom PC, the current Zone could be detected by an expression in a file info panel template definition, and cause different templates to be used that way. I've never tried to do that, so there'd have to be some experimenting.