Hi John,
I added one suggestion re: pages-in-a-category to your work page. Not sure it was a particularly helpful one, though. Looking through your other possible metrics, I see ways of gathering most of them via database and/or API queries, but I don't know of many tools (other than the ones you've already listed) that provide a GUI interface that allows you to get those data without writing some queries or scripts yourself.
For queries related to Wikidata, you might try the new Wikidata Query Service (web interface[1], manual[2]). And if anyone you're working with knows any SQL or a scripting language like Python, you can gather most of your participation metrics (pages edited, etc) via Quarry[3].
If you need a particular query run on a one-off basis, like "tell me how many of the users in this list have created an article in this category", post a request to this list and someone here may be able to run it for you. If you want to learn how to run queries yourself, I can take an hour to get you started. If you're able to take some extra time now to learn the ropes of SQL, it will pay off in the future. We are blessed with a bunch of awesome research tools, but as you've discovered there will always be questions that you want to ask, that there isn't a tool for.
Hope that helps,
J