If you're interested setting on your own web app, it appears NeoCat's code for arduino-tweet.appspot.com is on GitHub. I don't understand if the code is open source or not. You could ask @NeoCat on twitter if you could use it. Here's the link:https://github.com/NeoCat/ArduinoTweetLib-server
Personally, I don't know much about setting up and hosting web apps, but I would consider trying it (with NeoCat's permission, of course). There is still the matter of modifying the Arduino Twitter library to support a server different than arduino-tweet.appspot.com, but I believe that could be done.