This was a great chat, with lots of good comments and ideas.
One of the best ways to get engagement out of your community is to offer up some form of a contest. There are hundreds of different ways to do this, and there are obviously best practices at work by some of the best. However, before you start any contest of any kind, make sure you’re aware of the Terms of Service (TOS) of the platform you’re using if you’re doing it on an unowned property (Facebook, Twitter, etc.).