Another suggestion. We just got these in for a different project and they are plenty bright, but the LEDs are tiny pinpoints so I don't know how well they'll diffuse into a larger square. Also, I don't know how long the batteries last, but Amazon says 48 hours on one set of three AAs.
You could stick the battery pack in an easily accessible pouch in a sleeve or pocket, and run the wires to the places where you need light.
Look at the customer-submitted images, someone used them for a Mass Effect costume.
 oh, looks like they come in green too: