tl;dr - Find an application you like to make, and remake it in every new library you want to learn.
I don't think that is productive. So, after some serious trial and error, I figured out what I think is the best way to write in a new library.
Find a simple tool you enjoy building. Something that has the basics of a simple application. API support, data binding(or lack of), repeating elements, promises, etc.
Make sure you can build it in your first library with your eyes closed. When you can do that, try your hand at building the exact same tool in the new library.
Compare each step with a feature you are used to, and use google to help you find the best practices that compare to them in your new library.
In Angular, you keep JSON data and logical code in services, and make API calls from a factory. How would you structure that with Backbone? Would you keep your logic inside a model?
When I am learning a new language, my GOTO project is always a SoundCloud music playing multi-page app. It is a great project because when you get a player where you can search, save(to local storage), and play music, which covers a bunch of different topics needed to master a library. And if you work on it enough, you can have a product that you would actually use. I actually still use the one I made in Angular. I enjoyed the design, and the efficiency so much that I just kept working on it and making it perfect.
Lastly, post these projects in open git repositories. Find skilled people who write in those languages that don't mind looking at the repository. They can help you improve your code, as well as tell you about common pitfalls.
Good luck making yourself marketable and well rounded.