Right, well, I'm sure you're all breathlessly awaiting developments on this hot story. Here's the latest: the back panel on the housing isn't, strictly speaking, a back panel.
It's a series of panels, held in place by a clip across the top, and one of these can be removed to accommodate the plugs. I will be checking this out when I get home to see if this solves the problem.
Like you say, Dan, it's a good day when you learn something.

Great success!! Well, almost. I got the card installed but lost the picture on the screen!
It started up okay but the No Signal message appeared. The screen went blank, and the power light went from green to amber. Judging by the noises though everything else was starting as normal. Took the card out, screen is fine again.
There is of course the cable with the 4-pin plug, but I still can't figure out where the other end goes. As far as I could see the card was securely fitted into the slot.

Yep, it's finally done. All in, rigged up, and working properly.
Turns out that what I needed was a DVI-VGA adapter to connect the screen to the plug on the card. A kindly tech dug one out of his box of magic tricks, and now we're flying!

I found a couple of articles afterwards that explained the problem.

http://www.thesmallest.com/lessonettes/dviandvga.html

http://en.wikipedia.org/wiki/VGA

http://en.wikipedia.org/wiki/DVI

http://www.datapro.net/techinfo/dvi_info.html

You'll have to excuse me now. There's a collection of Scarlett Johansson photos that are going to require a whole new enchanced scrutiny.

Great news. Enjoy!