>Also, I have always wondered if there's a way to translate these shapes to strings for quick "mental algorithm" matching. Something like, "5, left turn, 3, right turn..."

I was once measured to have abysmal spatial reasoning (which is probably backed up by poor hand-eye coordination and sense of direction) but I had no problem doing molecular geometry and group theory, I suspect it was because I applied logic rather than visualisation to compensate. (I am terrible at walking into an empty place an imagining how I might want to fill it)