I haven't been able to track down a thread pointing to how I would actually get essences for the generator. Are they purchasable? If so, where? I saw something about farming egg nurtures for essences, but all I've been receiving from those are scales. Any advice?

You can get essences through nurturing, battling, or from opening mission satchels. All these have a very rare chance of dropping an essence though, so you'll need to do a lot of the action just to obtain 1 essence. I believe you can also get them from playing Jinxie's Jamboree, but I'm not sure about the drop rate, since I personally never played that, but my guess is that it's hard to get essence from that too.

You can also buy essences from the diamond shop (using diamonds), or from other players on the trade broker (but it can get expensive).

Great to know. Thanks very much!