We had the same problem. The __c parameter cannot be found through the API. We worked around this by capturing the parameter manually once per account. This way, we can build deeplinks for several areas of the interface, which is very helpful.
The downside is that Google doesn't commit to keeping the URLs the same forever. However, for the old interface, URL's have stayed the same for a long time.
In any case, an official way to do this via the API would be much appreciated.