You can always deal with it the expensive way. A DUO or Radiance VP are specifically designed to deal with this kind of issue. They have seperate audio out HDMI ports that may optionally be used to separate the audio from any HDMI source.
For example in my bedroom I am using an HP x280N through a DUO to Panny Plasma. The audio is seperated in the DUO and sent out a second HDMI port from the video HDMI. When I turn the TV off I get about 30 seconds for the whole chain to re-handshake and that audio continues. I do a similar thing with my 92" Mits. I send the HTPC with Ceton to the Radiance and it splits audio and video to their respective destinations and audio continues with the display off.
Both the Panny and 92" Mits are power hungry and for playing music they are overkill. I am considering small seperate HDMI displays to sit in those rooms just for music selection as both Video Processors support dual displays in addition to the separate HDMI audio out
Mits WD-92840 92" DLP - Lumagen Radiance XS, Martin Logan Motion 40s, Ascend Sierra 2s
Older 58" Panny Plasma -DVDO DUO, JBL Studio 530
Pioneer AJs, PSB Images, Usher S520, JBL HLS-610, Definitive SM45, MusicHall Marimba