After some more digging (including looking in Ember Inspector, which was showing my original route as valid) I found that if you call App.Router.router.recognizer.names
you can see all the routes that transitionTo
can call.
Because interactions is a resource I could call it by itself and pass the models in, this will create the route I expected.
The final code then was just;
transitionTo('interactions', show_model, report_model);