This is not an easy question, as are many other questions about coauthorship. To an extent, all answers will be opinion-based.
I am in a similar position. I work in industry but advise many of my wife's clinical & biological psychology students on statistical matters.
My personal cutoff point is somewhat later than yours seems to be. I'll happily invest three or four hours to help students clean up and understand their data, do some exploratory data analysis and plots and some simple models and release them into the wild with an initial R script. If that is the full extent of my engagement, I would be uncomfortable with coauthorship (but an acknowledgement would be appropriate).
Often, things go further than this. After this initial session, I'll code up more complex analyses, more sophisticated graphics, maybe research special models or approaches and/or read up on stuff. This usually involves some work on my own, multiple email exchanges and more personal meetings. At this point, we usually agree that I get coauthorship, and as you write, this means that I'll be a lot more involved in the rest of the manuscript's lifecycle.
I'll usually not write up the statistical methods section as you appear to do. My take is that the first author should have full ownership of the manuscript and should essentially understand everything in sufficient depth to describe even the statistics himself. After all, he will be the one to present it at conferences and/or thesis defenses. (It helps that psychologists get a lot of statistical training.) Of course, I'll go over and correct the methods sections, and I happily rarely find that the student fundamentally misunderstood the statistics.
If things have progressed far enough for me to be a coauthor, I'll usually be quite involved with the rest of the manuscript, too. I am rather anal-retentive and will happily nitpick the entire structure of the paper, the internal logic, grammer and punctuation. I don't know whether nitpickery is more generally a specific skill of statisticians, though... Of course, in maybe half of all submissions, reviewers ask about the statistics, and I often have to revisit the statistical analysis and/or at least its description.
Coauthorships arrived at in this way are actually pretty low-effort for me. Other people on the author list have spent weeks interviewing people in African refugee camps, juggling noxious chemicals in a lab and/or digging through prior publications. I, on the other hand, spend maybe one full work week altogether (sometimes more), sitting in a comfortable chair at my computer with a cup of coffee within reach. It's comparisons like these, and I'd guess that most statistical engagements are similar, that make me uncomfortable starting to discuss coauthorship after only one hour.
Laying down ground rules early on, as you suggest, is an excellent idea. Part of these should be how much time you can afford before thinking about coauthorship, whether this is 20 minutes or four hours.
One other thing, which the blog post you link to discusses, is that you as the statistician will need to understand the scientific context, so the researcher will have to spend some time explaining the situation to you. This time will need to come out of the initial "budget", since time does not grow on trees. Your client will usually try to handwave this away and insist that he only has "a little statistical question". This will usually not make much sense. If a client insists, you can always point him to CrossValidated for his "little question". If he gets a good answer there, great.