Thanks for the suggestion on the URL. When we eventually support accounts, we plan to allow you to start a screen session by simply clicking on a name from your buddy list so hopefully the longer URL will be less of an issue for frequent users.
Hell, when generating the url, just make a call to the api at http://tweak.tk so that you can display the short one side-by-side with the long one. Provided your codebase is well formed, a change like that should not be astronomical.
(P.S. Tweak.tk is really awesome. At least check it out.)