The Application Hang event means that Windows has decided that the application is unresponsive. Since the event is generated by the operating system and not the application, your options for getting additional information in the event are extremely limited.
This is what seems to be available on an Application Hang event:
Message: Hanging application %1, version %2, hang module %3, version %4, hang address 0x%5.
From:
http://www.microsoft.com/technet/support/ee/transform.aspx?ProdName=Windows+Operating+System&ProdVer=5.2&EvtID=1002&EvtSrc=Application+Hang&LCID=1033
If you believe the cause of the event is something that your application does (as opposed to something in the environment where the application is running), then instead of trying to pass info to the hang event, you should raise the level of log info to debug mode and look in your application's log file to see what it is doing just prior to becoming unresponsive.
If you lack logging information, or a logging framework in your application, then that is where you should be focusing your efforts. The upside is that you will benefit from better logging in the future as well. Use a logging framework however, so you can disable debug level logging in a production environment, when everything is running smoothly.