I did some poking around: it appears that the current RPI sound drivers (for on-board sound and HDMI) in Raspbian still limit Alsa to 48kHz. Fixing this would involve applying patches and/or kernel recompiling.
I upgraded my Pi to the 4.4.x kernel branch
sudo BRANCH=next rpi-update
which has these patches already applied. It appears that all rates up to 192kHz are now available on HDMI:
I don’t have the equipment to test, but this will probably work.
One word of warning: the next branch is not a stable release and in active development. If things happen to break, you can revert to the currently supported 4.1.x branch:
sudo rpi-update
@Brian: this is where the most recent action appears to be with HDMI audio on the RPI. They’ve moved on to multichannel, but fixed the bitrate issues first.