It works!
The test of my TweaK API wrapper script was a complete success! So, since it works, I can go ahead and share the website. Anyone who would like to use my code to get the shortest link on the planet can go to http://tweaky.tk. The page there will give all the information needed to use my script, including a link to download it. If you have an account on Dlvr.it, you can simply add Tweaky as a 3rd-party shortener by setting the endpoint to http://tweaky.tk/wrapper.php?link=@URL@. Also, Tweaky works very similarly to the shorten function of the TweaK API. You can send an HTTP get or post request to http://tweaky.tk/wrapper.php with the link parameter set to the long link you wish to shorten. Tweaky will return only the HTTP response code, and, if the long link is good, the short link returned by TweaK. Enjoy the shortest links on the planet, courtesy of TweaK and Tweaky.
Update
The TweaK API and website no longer work, as they have been replaced by Freenom's Random Domains API, allowing for 5 times the domains, and therefore 5 times the short links. The Tweaky website and wrapper API have been discontinued, as anonymous registrations via the Random Domains API are limited to 25 per day. Any references to broken links to the TweaK API and the tweaky.tk website are preserved for archival purposes only.