Should one stick to the organization of a paper while teaching a subject?
Even if the authors are excellent writers, there's no reason to assume that the organization the authors chose as best for an audience of specialists is also the best one for your class.  (At least in math, it's very rare for the editors or reviewers to call for organizational changes.)

I'd feel quite free to present the material differently if I thought a different order emphasized the points most relevant to my students, would be easier for them to follow, or I just preferred it. Indeed, I think there's some benefit to intentionally giving a different structure, since I think students benefit more from having access to multiple explanations than from repeating one slightly better one.