I gave that a try just then, had some other stuff that needed doing first. It's a good idea, but on boot the machine still goes to its VGA port. I could get into its BIOS with lucky clicks of the Delete key and the monitor power switch, and there are some options for PEG display which I don't have, and allowing the IGP to sleep, but nothing that might help.
Then I noticed that my old Acer LCD has a VGA port on it, as well as an DVI. Aha! So, using a VGA cable it all works. And I still don't understand why the HDMI output rates as "second class". It may be, as suggested that the adapter was causing problems. Also, the monitor displays an overlay at each boot/awakeining saying it's 'auto adjusting' whatever that may mean. The VGA signal seems a bit 'wobbly' at first, but it's only a 1080 signal, looks fine now.
I've got the latest F4 BIOS on the Giga board, and seen no other complaints similar to this, so I'll get another HDMI-DVI cable, see if there's anything I can change on the monitor and leave it at that. It's about time I got a 27" or 30" anyway...