A solution
I'm happy to report that I've found a solution. It's not ideal, but it does work. I asked Light and Motion for a solution, but they're yet to get back to me. Other forum searches web-wide suggested some options, and a combination of two has done the trick.
Spanky_Ham was sort of on the right track with shielding the cable but didn't mention HOW to shield it. And just shielding the cable wasn't enough. I still needed space between the light and the computer.
So, as shown in the images, the solution for my problem lies in separation AND shielding. The distance between the light unit and the computer is around 180mm. Reducing this gap by even 10mm resulted in interference again. This is almost as far apart as I can manage on these bars. Bar width overall is around 700mm. I'll move the computer to the stem for day rides (it only takes a minute or two), as it's a bit more vulnerable out there on a limb.
The widget near the battery is known as a ferrite choke or ferrite bead amongst other names, and suppresses high frequency noise in electronic circuits. I bought a pair from Jaycar Electronics for about $9, but if you've any old computer cables lying around, these are often near the end. What surprised me was that it didn't matter where on the battery lead I put the choke, it still worked. But then I haven't a clue about electronics, so maybe that's obvious to someone who does. And yes, the battery is a tight fit, but it works.
So I hope this helps those of you out there who like to record your stats after dark. And the solution should work for LEDs too. Can't help with the halogen downlight problem though. I can only suggest pulling each light out and putting a choke between each light and its transformer, on the 12V cable.
ps. Response from Light and Motion early this morning was "With the HID Light the most accepted form of getting around this problem is to mount the light on top of your helmet." Sure, that's a solution, but just not the solution I was looking for.