You don't remember your exact cab dimensions yet you say it 'wasn't much more' than 1 square foot?
Funny but you are proving my point exactly, without exact measurements, any kind of extrapolation is useless.
Unfortunately the picture of your light fixture shows your cab is NOT a little more than 12" x 12". That light fixture is at least 18" long if not 20". I have a similar light fixture in my bathroom and it's 24" long.
I will use this as an example to show how far off people are when they 'guess' or approximate things.
EXAMPLE
I will give you the benefit of the doubt that your cab is 18" x 18". Feel free to get the EXACT measurements in inches of your cab to correct me. If you come back and say something like 14" I would ask for a photo of the inside of your cab with a ruler on the bottom of the cab.
(images below from your thread/gallery support my 18" estimate)
Square footage calculation
Lets say your cab is 18" x 18"
To calculate the square footage of your cab you measure the width and length (depth) of the floor of your cab in inches. You multiply these two numbers together and divide by 144.
18 * 18 = 324
324 / 144 = 2.25
So an 18" x 18" cab will have 2.25 square feet. This is not 'a little more' than 1 square foot.
A 16" x 16" cab gives you almost 2 square feet.
16 * 16 = 256
256 / 144 = 1.78
Watts per square foot calculation
Now lets take your 'a bit over 200 watts' and call it 220 watts (that's 10% over, ie more than a 'bit')
Take your 220 watts and divide by the square footage of your cab (2.25). This will give you the wattage per square foot.
220 / 2.25 = 97.78 watts per square foot
Heck even 16" x 16" only gives you 123.60 watts per square foot.
220 / 1.78 = 123.60 watts per square foot
Neither of those are anywhere near 200+ watts per square foot.
If we use 210 watts in this example, it only makes your watts per square foot go down.
18" x 18" (2.25 square feet)
210 / 2.25 = 93.33 watts per square foot
16" x 16" (1.78 square feet)
210 / 1.78 = 117.98 watts per square foot
Conclusion
None of this is to put your grow or contribution down, it's just to show how calculations can vary greatly when people don't have accurate measurements. Which goes back to one of the motivating factors for building a cab that measures 1 square foot (12" x 12").
Edit: This image from your own thread/gallery, with a yardstick in the picture, shows your bin itself is 18" long (supporting my 18" x 18" example above)
Edit 2: This image, which is also from your thread/gallery, shows that your light fixture IS 24" LONG with the decorative outside (like the one in my bathroom).
Removing the outside and using only the 'guts' of the fixture, like you did, only reduces the size of the fixture to about 18-20" (prolly closer to 20")