How should a drop in GPA be presented positively in a Statement of Purpose?
Personally, I would avoid making excuses for a drop in grades. They are what they are.

Instead, you should highlight the independent research you did and published. That's a huge achievement for an undergraduate. If it's obvious to the reader that you put a significant amount of effort into that research and learned a lot, that should outweigh the fact that you didn't learn as much in class.

If the grad school programs you are interested in do still have a coursework component, then grades will matter more than they do for a research-only course. But if they're good enough, research experience will make up the rest. That, glowing letters of recommendation from supervisors, and a good interview are worth more than perfect grades.


  Don't waste words making excuses. Show you are emotionally invested in your research. Make promises. 


Anecdotally, my GPA tanked from A- in my final undergraduate year to B (overall) in the first year of my Master's program. I had a tendon injury and couldn't write for nearly 3 months, so I only just scraped through that first semester with a C average. Way behind on my research project, I put that ahead of my second semester papers and did very well in the research but with average coursework. Those grades got me my dream PhD job, and I haven't even finished my Master's thesis yet. I never mentioned the injury because no-one ever asked about my grades.