Have you calculated whether you can cram enough LEDs into that space to get
the same brightness level as the discharge lamp? Or are you expecting to learn
from the test?

I'd like to point out that is no such thing as -- nor can there be -- a white
LED. LEDs are necessarily limited to a narrow band of wavelengths. * All (???)
white LEDs are (I assume) a blue LED with a yellow-fluorescing phosphor. **

This /looks/ white to the eye, but the red and green wavelengths needed for
color reproduction aren't present.

Unless your white LEDs contain red, green, and blue LEDs, I don't think this
is going to work.

* This is actually a good thing if one is trying to match a specific color
space, and you can manufacture LEDs whose wavelengths correspond to the three
primaries.

** I'm thinking of indicator lights and such. Lamps to replace incandescent
lighting would necessarily have to put out red and green, or colors wouldn't
look right.