This seems hard to do in new ember router because ember is working hard to prevent you writing code in this style. Rather than access an instance of the router (or anything else) via App
your ember application code should be working with properties that have been injected at runtime by the framework. As @sly7_7 mentioned above, your view will have access to the controller and controller can trigger a transition like:
view.get('controller').transitionTo('state')
Depending on how your third party library is working, you might do this by triggering an event in the dom (handled by the view) or by registering a callback when the view is rendered from within didInsertElement
The main thing to remember is that App.anything-in-lowercase
is generally bad practice. Whenever possible try to let the framework take care of instantiating and wiring together your application classes.
For more detail, see the notes on this commit: https://github.com/emberjs/ember.js/commit/5becdc4467573f80a5c5dbb51d97c6b9239714a8