What should one do if they've discovered a "breakthrough" but lack academia credentials?
I see a few approaches you could take (or some combination):


Write up the idea as a white paper and submit to http://arxiv.org (or something similar). This gets the idea documented, public, timestamped, and allows people to easily cite it.
Reach out to researchers in the field to see if they would be willing to help you form a scientific paper based on your idea. Not all professors are scary!
Submit to the industry track of a research conference if you have an industry background (if not, then maybe a workshop). Some conferences elicit papers from industry that can get your idea out there, generate discussion, and allows you to get feedback. These tracks are often less competitive and very open to non-researchers. For example, Software Engineering In Practice at the International Conference on Software Engineering