Good suggestion. I already tried setting it to max, but it only takes effect if I set the STB to output stereo (which is not transmitted over HDMI). On multichannel output the volume control is disabled, and a pop up box informs me that I should use my receiver to adjust volume.

I should also add that I've tried connecting the STB to a Denon receiver I got laying around from a previous setup. The volume levels remain pretty much constant on the Denon regardless of the audio on the broadcast. So I'm pretty sure that the HD621 or G68 is to blame here.