Disclaimer: I apologize that this question is so long. I have added code as I have explored suggestions made here and done additional research since asking
The immediate thing that comes to mind is, take a look at log4j. It's an open source logging framework that's very widely used in all sorts of libraries and applications.
Edit:
java.util.logging is the basic API. It really doesn't do anything you don't tell it to do, explicitly, in code. log4j is a library with full configuration facilities and other goodies. It sits atop java.util.logging and expands it with functionality that is much easier to use than the (relatively) low-level java.util.logging.