If you wanted to fully customize your notifications, you could write a plugin to use the CMailApi class to send notifications exactly how you want. This won't integrate with the existing notification architecture, unfortunately, so having some plugin API interfaces that allow you to hook in to the existing architecture isn't a bad idea.
If you're running a licensed version of FogBugz on your local machine, you could tweak the source code to see if you could get the data you are looking for into notifications. You can modify the FogBugz source code, found in src-website of your FogBugz installation, and then run build.bat from your installation directory. Look at Function GetEmailSubject() and pay attention to where it gets called. Unfortunately, we can't provide much more detailed support for customizing the source code base unless we're working on a mission-critical situation. However, you're free to poke around to see if you can't get it work the way you want.