Thank you for posting on the forum. Glad that you finally discovered the name of the condition.
I haven’t personally heard of any link between a stammer and VS. My gut instinct is that they are completely separate conditions, but I guess anything is possible given the bizarre nature of Visual Snow Syndrome. I’ve shared this on the Visual Snow Facebook Group so perhaps someone else can give you a better answer.
In terms of the words moving, what you’re describing is a form of pattern glare or visual stress (check out the symptoms page). It’s a common symptom of dyslexia and VS. Hopefully the dyslexia test will provide some insight on exactly which condition is causing it; it may be one, the other or both.
Hope that helps!