It's probably not good form to answer your own questions, but this forum seems very quiet...
If anybody is experiencing the same lag problems, then things can be made MUCH better by forcing the picture quality to standard, rather than high quality.
I've noticed that the command from the remote is issued without much delay but you don't see the effect on-screen until 7 seconds later, as that seems to be what has been buffered. I guess high quality just uses a big buffer - not sure exactly how that can be worked around. Discarding the buffer when a command is issued would only help on some occasions, I think.