Writers I work with sometimes interpret the 6 sentence/200 words rule of thumb a bit too strictly at the beginning of the process. They imagine I've defined a paragraph as precisely as a Shakespearean sonnet (14 lines of iambic pentameter, with a couplet at the end). As an exercise, it is perhaps worth trying, but only to see that 200 words in 6 sentences makes for very long sentences. What I'm saying is: in most cases, you will write at least six sentences and at most 200 words. And I'm suggesting that you make such a paragraph in 27 minutes. The dimensions of a paragraph are not a frame to stuff words into but a space in which to make a limited number of moves or gestures. I recommend you view the paragraph as neither a set of requirements nor a set of limitations but as a resource. Or, better, a space of freedom.
The key sentence provides you with what Ezra Pound called "a center around which, not a box within which"* to write your paragraph. The space of the paragraph opens up along dimensions that are set out in that claim. If the key sentence names a particular event, your paragraph will describe it in detail. If the key sentence identifies a controversy in the literature, the paragraph will present arguments on both sides. If the key sentence says you conducted interviews, the paragraph will tell us with how many people, under what circumstances, with what questions in mind. When you focus on your key sentence, you will find that twenty-seven minutes is plenty of time to compose yourself. You will feel the intellectual space around you as comfortably proportioned. Part of the art of writing a key sentence is to conjure up this space in which to work.
*Update 27/11/16: I originally came across this phrase in Rosmarie Waldrop's introduction to Curves to the Apple (2006), where she calls it "Pound's postulate" and uses it to describe her use of the prose poem as a form. That form essentially consists of what I call "paragraphs" (although they are, of course, more poetic than the paragraphs academic writers normally produce). It turns out, however, that Pound was not talking about literary form at this fine-grained level. Though I'm sure he would agree that the "form" of, say, a sonnet shouldn't be a approached as a box to stuff a certain amount of syllables into, Pound was talking about how to organize a literary magazine. Specifically, he was offering advice to Robert Creeley about how to run The Black Mountain Review.