Some thoughts:

One thing that went well introducing sliders was something similar to the handout you envisioned: give the features of a particular function (in Algebra, a quadratic with certain roots) and play with the a, b, and c sliders to get those roots.

It doesn’t work yet, but if you try to convert a polar function to a table in Desmos, the error message reads “We don’t do the right thing for tables with independent theta YET” so at the rate they are adding new features, your big fat table could be in Desmos?

I lost a complete day in one class for reasons similar to those of your supplementary handout; I basically gave out a little guide to Desmos with some problems at the bottom and it wasn’t clear to my students (or me, I suppose) what the point of the 45 minutes was. Much better was a different class where each new feature was followed by a question where they were asked to use it, even a pretty straightforward one. For example: click on the graph of a parabola to highlight the points of interest and restrict the domain so that the image of the function is nonnegative.

I have kind of a silly question about kids bringing in their own laptops. I allowed it for a bit, but for a while Desmos was so new that it wouldn’t work except on the newest version of Chrome or Firefox (this was around October). Any such issues?

Anyway, great post that gave me a lot to think about, thank you.