What you described is exactly how I experience things in my head as well, including that redrawing part. I've noticed though that as I've spent years learning

What you described is exactly how I experience things in my head as well, including that redrawing part. I've noticed though that as I've spent years learning Japanese characters, I am somewhat better at visualizing them in my head. I can see (or "feel", as it's not really visual exactly in the same sense as seeing, although they are not just concepts but have spatial locations) whole subcomponents at a time instead of having to plot each line.