I've experimented a bit more.
I haven't tried every mode, but I've tried over a dozen and I've only found two settings that work with this particular adapter.
puts the adapter into 720p60 which shows up in X as a very poor 576x416
puts the adapter into 1080p60, which gives a slightly improved 960x704
This is far less than the adapter is capable of - as in my Kubuntu laptop I can drive the HDMI cable up to 1366 x 768, also if I use a HDMI to DVI cable on the Pi then I get a resolution of 1366 x 768.