I haven't gotten any further. Occasionally I manage to get a screenshot to work. I can send colours and effects to my ambilight from my phone, but HDMI input does nothing. The vast majority of times screenshots won't even work, failing with the result "no picture found in ssh traffic, stop hyperion before taking a screenshot". This doesn't seem possible, as if I stop hyperion, SSH disconnects so I can't request a screenshot, and if I reconnect, hyperion has automatically started again. I have tried two different grabbers, one of which has the recommended UTV007 chipset, and still nothing.
I have heard recommendations that I use a powered USB hub instead of plugging the grabber into the pi directly, however I have seen other people's setups work without this, and I can't find a powered USB hub available anywhere (most hubs just take power from the device anyway...)