How do I appropriately use inline citations for multiple quoted paragraphs?
From what I've seen, the only situation in which you would use a single citation following multiple sentences is if it's obvious that you're quoting that source verbatim AND the quote is uninterrupted. If you're using your own terminology OR the quote is interrupted, you should cite each sentence separately.

This becomes obvious when considering the purpose of a citation. Citations are there to answer the question, "who said this?" If you're quoting someone verbatim, and it's obvious you're doing so, then you only need a single citation, as the reader will infer that it applies to the entire preceding quote.

On the other hand, if you have multiple claims throughout a paragraph, after each claim the reader will wonder, "what's his source for this?" In most cases, you will be using multiple sources, and you will have a mixture of references. However, even if you have a single source for lots of claims, the reader will still wonder after each claim what the source is. You should tell them the source of each and every claim separately.

The exception I've seen—and that my advisor requested I use in my writing—is in the instance of a single logical thought pattern being followed throughout a paragraph or set of paragraphs. If you're describing someone else's work, it can be justifiable to state, "the following is an overview of Bob (2007)", or something to that effect. From my experience, though, that usually only happens in review articles.