I presume by the "summary" you refer to the hover preview?
Our current vision was more something along the lines of "allow users to provide an explicit abstract of a post that shows on hover and in other contexts where summaries are useful"
I'd still like the ability to make the explicit abstract just read off the text after a certain point, but I suppose it would require a lot of work to support that functionality.
Headers are very common on Less Wrong, unfortunately, they interfere with the summary by taking up most of the space. I'd suggest the creation of a feature to mark certain content as a header which would then exclude it from this summary.