I had discussions with Thomas on this issue (off list) and the final conclusion was that there was no way to do what I wanted because Java (under the hood) is not respecting the Linux window managers (in this case Fvwm).
I found that when I replace the Java widget with "something else" (like XEyes, or whatever) I got the behavior I wanted. I still have a -tiny- bit of hope that (inside Java) I might be able to refuse keyboard focus, but my first stabs at this (like "setFocusable(false)" on the main GUI container) haven't yielded anything.