Today saw the culmination of about a month of preperation. Acquisition of wood, finally, and consolidation of innards for the lightbox!
Experiments, from last month, demonstrating the CCFLs in action:

Various sketches and measurings!
There was marking up:
A few pieces had to be recut, but eventually the sides and backing were in place. I was able to get some nice pre-coated stuff that had a lovely glossy white finish on it. Perfect for reflecting, and acts as a makeshift heatsink to conduct away any excess heat from the tubes. Here it is in a test setup, showing off the extended leads on the lower CCFL:
Since the cold cathodes used to provide the light run off a 12v supply, we needed a 12v transformer. This was duly acquired, and for the hell of it run through a big beefy mono audio jack (which will handle that kind of voltages fine, and gives a lovely heavy -k'chunk- noise when you plug it in. Looks the business too. The plug's connected via a MOLEX plug to the inverter.

Here are the innards assembled. Note the inverter for the CCFLs at the top, and the spacers to support the perspex at the sides. The tape holding the tubes in place is temporary, as this is a 'working prototype', so to speak.
And finally, the 'finished' article, with the partially-frosted perspex in place. The diffusion this provides ensures a more even light distribution (although the camera doesn't really show it). More frosting will be added when I can be bothered. (The masking tape at top and bottom is there for anti-scratching when seating the lid.
Done!