Not sure what took Twitter so long, but at last, their official Twitter app has been updated to be optimized for larger screens.
However it hasn't been officially released yet. The APK for the tablet version has been leaked. As expected, on the Nexus 7, it looks much better than the standard mobile version. When in landscape mode you're given two columns instead of the standard one. The right column can change depending on the situation too. So if you're viewing someone's profiles, it can change to show the users photos.
With this being a leaked APK there may of course be some bugs here and there so download and use at your own risk.