Should one distinguish between meta-thinking and meta-meta-thinking?

I think not. I feel that it would be reasonable to define meta-thinking as "thinking about patterns of thought", with the content of these lower-level thoughts having no particular importance. They could be object-level thoughts or meta-level thoughts; in either case reflecting on their patterns would be considered meta-thinking.

This also fits my experience with meta-thinking skills on LW. I've found that techniques like Hug the Query can be applied regardless of the current level of abstraction.