The app takes a real long time to load up but does eventually load up.
I noticed in the console that its trying to load the libraries from the wrong location (after it already loads it from the correct location) with a message that either states the jar has expired or cache entry not found.
The library files are all located in a /lib subdirectory under where the main jar is located.
As you can see from this message the jar is loaded from the correct place:
Do you means the app ran fine the first time, but does not on subsequent runs?
Did this app run fine with some previous version like 6 or 7 before 7u4?
Would clear the deployment cache help? To clear, use Java Control Panel or run command line javaws -uninstall.
If yes to any of these questions, then probably it is a bug and the best way is filing a bug report against JRE 7u4 deployment attaching full tracing details.