Did you measure, though, that the staff was happier or more productive? Did any meaningful change occur as a result of the requests to use Slack differently?

Looking at your graph, it's not really clear that anything has changed significantly: when did the change get implemented? Is a couple weeks' change in activity a result of a couple of loud employees going on leave? There's such variability there that it's hard to say that anything has really changed.

I agree that a formal analysis isn't always necessary, but you don't appear to done _any_ here and are then couching a suggestion to try something on Slack as having measured something. That's just bad science! :D