The other thing that can help to hide the teel is seamless incorporation of quotes. If a quote is built up to, or used not as part of a sentence then it stands out and this makes the essay look uber structured, and having little or no flow. By using a quote as though it is your own words, and in such a way that the sentence is not disturbed at all means that although it is clear that you have quoted the text, it doesn't look like you just stuck a quote in because you needed one.
I agree, when i write i try to avoid the " X supports this view when he says Y ". By incorporating the quotes into your writing you are essentially placing the Evidence section into the Explain section which adds to the fluency and also coherence.
To answer the initial question

Other than reading high level essays (which I think is the best), perhaps attempt to incorporate the evidence into the explain part and go through how you did this?