I have never had the chance to try JMVC but with CanJS is easy read the docs and the API
That documentation doesn't point out anything helpful with regards to accessing controller instances when you only have DOM element references available. Also, you are making several broad assumptions on what the TS is trying to accomplish with his application. Routing may not be applicable here at all. (Besides, treating routing as a golden hammer and using it for each and every interaction means you will be pushing a lot of history states into the browser all of which have to be undoable to preserve integrity of your application state, should the end-user use the browser's back button. Madness!)
Aaron, have a look at the can.Control.plugin. It allows you to retrieve controller instances from DOM elements. E.g. given a control of type app.controls.Control that is present on a DOM element with CSS class child, you can select it like so:
- can.$( ".child" ).control( app.controls.Control );