So the project is short-handed, but wants to take on scouring analytics to start packaging common things people are doing with the software.

If you're too busy to do this "right" why bother? Are you hoping making more shortcuts will increase adoption?

Current employer doesn't much care about these things, but last employer did. Having shared this thread with their IT folks, they've decided to cut people off from homebrew while they figure it out.

I guess costing yourself users is one way to free up some time.

As I wrote we’d be very grateful if you had any suggestion.

Have you tried getting donations for the project? Have you tried joining a foundation that supports open source projects (like Apache)?

Yes we recently joined the Software Freedom Conservancy so we can now accept donations.