The curve is a bit steep but once the things start clicking you productivity goes through the roof. You'll be able to make game prototypes in a few short hours.
I admit that building 2D games with unity is a bit of an overkill but the fact that everything just works across different platforms makes it well worth it. I originally developed games using Java and a cross platform framework called libgdx. It was fun till you needed to implement things like cross-platform advertisements and IAPs. With unity you know that the support will be there for the foreseeable future and no other engine comes close in terms of the available free online resources.
I love the Unity asset store and I use it a lot for graphic assets. I intend to get back to Unity when I feel a little more competent and not feel like I need a whole bunch of third-party programming assets to do what I want to do.
The easiest way to learn unity (or any other new framework/engine/language) in my opinion is to recreate the project that you've already built. And you have one.
I just paid for your Android app and had a play with it and left a review. It is more polished in-game than I expected from the Google Play listing; the icon for the app looked a little bit 2009. So I was pleasantly impressed with the game itself. Great work!
Thanks for the links, I'm gonna check out your games!