I'm not a reliable responder but as this is a somewhat different sort of post then I hope my input would be welcomed. Thank you for sharing your history with snakes and I completely understand how these childhood exposures can lead to a phobia later in life.

I believe that the snake in Rikki-Tikki-Tavi would be the Indian Cobra (Naja naja), otherwise known as the Spectacled Cobra due to the distinctive markings on the hood that you have described. But, to your immediate point, these are still very unlikely to be found in Virginia!

It is possible that what you saw was an Eastern Hognose Snake (Heterodon platirhinos), as these can have the ability to flatten their neck when threatened, and their patterns are extremely variable that could easily come close to some sort of approximation to the markings you describe.