Sorry for disappearing for a few days there. I'm in the midst of Finals Week at school, so things have been a bit busy. I'm back with another thought about series, though.
Upon further reflection, I realized that there was a category of novels that I was leaving out of my original analysis for ongoing series. I don't really have a proper designation for it yet, though it's probably a more accurate representation of the independent style.
See, there's this whole sub-genre of stories like The Dresden Files and a lot of mystery novels, such as the works of Agatha Christie, where you have a single protagonist spread out over several books, but the stories are otherwise generally unrelated. Sure, you might have a character here or a plot element there that played a minor role in one book take center stage in a later one, but that has more to do with the author mining earlier works for inspiration than it does with an effort to craft an overarching, interconnected tale.
With this in mind, I suppose it's worth re-evaluating the different designations I provided and/or re-categorizing some of the works that I filed away in that post (Harry Potter and The Lord of the Rings especially.) For now, though, I think I'll just leave off with the brief recognition of my ignorance above.