Sorry the Oz forum is very quiet these days. Since no other responses I thought I'd chip in.
Unfortunately you ARE little overestimating most plants' ability to reproduce that fast. I can't think of anything that would go from seed to flower in a week.
Your best bet would be something like cress, or even better, sprouts (the type people eat). being legumes, they germinate quickly and you may even find some would reach leaf stage (nothing further).
Nothing sophisticated is needed, you can grow them in a dish on wet cotton wool in a well-lit situation, even a bright window, but since the plants tend to follow the light source, you are right, the light might need to be better controlled. In that case, something like a fish-tank set-up or at least with a constant directly overhead light.
You might need to photograph the un-germinated seed first in situ, and quietly start to germinate some off-camera to replace with as that process will still take a couple of days. Pre-soaking legumes in tepid water for a few hours, helps.
Dunno what else to suggest