I have discovered the joys of the Dremel.
Spent this morning in the school DT workshop and snipped out the car-dash socket along with much of the excess wiring. Knowing precisely nothing about electronics, never mind plasma balls, I got first, second and third opinions from my colleagues there. After some head-scratching, the consensus of opinion was 'Yeah, that'll probably work.' Always listen to the professionals, that's what I say.
Anyway, it worked, and I only burned myself a bit. Next job is to fit everything into the casing, basically as below, but with some gentle prodding and grinding.
Ooh, I feel all manly.