Maybe a bit late, but we designed a pretty awesome indestructible little GoPro light that will enhance all your GoPro footage. It's called the Sidekick - and we launched it on Kickstarter earlier this year. http://www.lightandmotion.com/landing/sidekick/
We support Francois - Xavier De Ruydts for many of his projects and he conveyed a similar interest in helping out with media acquisition for caving. http://globalnews.ca/ice-caves/how-we-did-it
An interesting concept, but in my experience not nearly enough light for anything but close up work. I film with GoPro3 Hero+ Black cameras in caves, using my own home built 2800 Lumen LED lights. Lumens are not the most useful measure as they amount of light going onto the scene is what counts. The quoted Lumen figures are just how much light the LED emits in any direction. So good reflectors make a lot of difference. For the very wide field of view of GoPro cameras, you need a wide spread and very even light source. I used frosted wide angle lenses/reflectors. Even with my very bright lights (I have 2 of them) I generally find that over 20 feet things start to get a bit dark for the GoPro. You end up with a lot of noise in the shadows. You can compensate for this to some extent by using the ISO limiting feature (I limit it to 1600) as above that the quality of the images is too grainy. Then post process if it is too dark to improve the footage. If you are shooting with a pair of cameras in 3D then it is even more important to have a lot of light, as the noise in darker areas is random, so it really spoils the 3D footage as there is no correspondence between the noise in the left and right images.
Most cheap LED bike lights are bright, but the beam is usually way too narrow so you just get a bright circle of light in the middle of the video frame. Using frosted glass in front of the reflectors can compensate for this to some extent.
I'm not saying that these sidekick lights wouldn't be useful. In fact a helmet mounted light which is compact would be great for point of view shots in smaller spaces, and perfect for close ups of any subject. Just don't expect to be able to film in large passages and chambers with this level of light.