It looks like HDFury AVR Key will do what is required for US$150.
I found this in a support forum: “It demuxes (separates) the audio from the datastream, repackages it into HDMI 1.3 or 1.4 format so it can be read and played back by a capable AVR, and combines it with 720p/1080p/no video to be sent to the AVR.”
I just hope it doesn’t introduce another layer of complexity into my system as it has its own UI (groan).