Guess I don't understand why you want to turn the display off? You can set the screen saver to blank the screen, and I believe MC even has a setting you can use. With backlights off, the power use, even on older LCD screens is pretty minimal, and certainly cheaper than hair transplants.
I had the same disconnect issues with two different receivers, A Yamaha with 3 HDMI inputs, and a Denon with 7 HDMI inputs: as soon as the display was switched off, I would lose playback...most of the time until I turned the display back on, some times the sound would go silent for 10 seconds and then come back on. I was never able to discover a pattern with either receiver. Been using a BB Zotac box with a Celeron SU 2300, NVIDIA ION with 8GB RAM with HDMI out as a MC server for 3 years now. For those times when I do not need to have the large display going, I went with running the MC server "headless" using either RDS or Logmein, power up MC server from another windows device ( surface Pro3), then I can use an iOS or android device as a remote control if I like, or continue with the surface pro . No worries about interrupted sound through the main HT system. I sometimes use the Surface Pro3 as the player, plug in my cans, and I'm set. This may not suit your MC use, but it sure "solved" my HDMI handshaking issues between components.