I just tried HDMI 3 with my Harmony One. The TV would not respond to it. HDMI input 1 and 2 are fine though as you mentioned. Have you tried having the H1 learn the HDMI3 button from the Mitsubishi remote?
EDIT: I see the Mitsubishi remote doesn't have direct access to the HDMI inputs. So I guess their database is right for the first two input but wrong for the third one. What about trying one of the other models that has four HDMI inputs? Maybe that will work.
EDIT: I see the Mitsubishi remote doesn't have direct access to the HDMI inputs. So I guess their database is right for the first two input but wrong for the third one. What about trying one of the other models that has four HDMI inputs? Maybe that will work.

























