After spending some time understanding the Ember Router, this ended up being pretty straight-forward.
In the route's "model" method, I simply use the params hash to deduce the proper model to use. This isn't so straightforward in my case because of the complex dynamic portions of my URL, but this was mainly just string-mangling code.
The other side of it is overriding the "serialize" method on the route. This does the opposite of the "model" method, and returns a hash of the dynamic "params" for a particular model object. This is used to serialize a model into the URL.
With these two methods implemented properly, it works beautifully.