I love the idea of sOccket and would like to buy one to show others in the community and promote this type of project. I would also love to "sponsor" one (or more) to help others. I am "into" solar ovens for similar reasons. I use one to cook in and start a conversation about solar energy, safe cooking in third world countries and how we can help others. I have also used freerice.com to empower low-income city kids to help others far away while learning words and skills.
Some thoughts about your project that I have not seen expressed that might improve it.
1. Have you looked into the quality of the LED light and how it interacts with the human eye? Is it good for people to use it to, for instance, read by, night after night? Could it cause eyestrain? I am a member of the International Dark-sky Association, and somewhere I heard a discussion about different types of light and which ones are best from the point of view of the eye (as opposed to portability, saving energy, and other output considerations).
2. In this country we have a problem of sleep deprivation. People stay up way too late on their devices, and especially those that emit in the blue light range negatively affect sleep by supressing melatonin. At an extreme, light at night has been shown to cause cancer, in people such as shift workers. Don't take this the wrong way - I am NOT saying it is not good to stay up past dark - but this might have some unintended impacts on family dynamics or health.
3. In pre-electric times using a lens to concentrate light on a surface (such as a book or sewing project) was widely practiced. I have a family heirloom lamp with such a lens attached so that the lamp flame "enlarges" in the lens. Also, using mirrors or other reflective surfaces can make a light appear brighter by "doubling" it. I have a big mirror that reflects a night light in my kitchen - when I come around the corner I see the reflection first, then the light itself - two for one, and I don't have to turn on the big overhead light to pass through the room without stumbling. How about somehow making a reflector available? Maybe it unfolds from the little light? This could also reduce glare, which is the enemy of good vision. You definitely want the light to shine on a surface, but you don't want to look at the lightbulb itself - that causes glare.
Best wishes on an innovative project. Suzanne deLesdernier