It sounds like this could be a cheap, fanless, diskless MythTV frontend.
If we don't want everything on the SD card, we could boot over ethernet from the backend server, or just mount an NFS server on the backend for most of our filesystem.
To keep costs really low, I would think about a Java/Android app for the remote control, connecting to a server on the RaspPi. MythTV already is controlled from simple keystrokes. It would be trivial to send these keystrokes over a socket from a tablet or phone.