Can you post the log files as described here:
http://kb.displaylink.com/269
I want to see what resolutions the screens think they are in.
Also, from the screenshot, it looks like you are in mirror mode. Do you get the same problem in extend?
It looks like the monitor doesn't support the video timings that are being outputted by the adapter, so in extend mode, it might be able to do the preferred resolution of the HP screen.
Wim