I have solved this.
The essential part of the solution was to add an external Jar file - in this RXTXcomm.jar.
I followed this http://www.vogella.com/articles/Eclipse/article.html#eclipseoverview
tutorial to get back on track with Eclipse. It has a section describing how to add an external jar file to a project. After that all the import gnu.io... references were resolved. It did seem to help to create a package and then a class file for the sample code.
When I added the external RXTXComm.jar (library) file, I referenced the "C:\arduino-1.0.1\lib" folder where the file resides. It might be best if it was put in the same folder as the project.
I removed all copies of rxtxserial.dll and RXTXComm.jar except from the Arduino IDE folder. BUT having Eclipse execute the sample code still works. I thought that it needed access to the rxtxserial.dll file. So I'm stumped on this. Perhaps its the PATH segment that lets it work.
The CLASSPATH is still: "C:\Program Files\Java\jdk1.6.0_25\lib;C:\arduino-1.0.1\lib"
The PATH still contains: "C:\Program Files\Java\jdk1.6.0_25\bin; C:\arduino-1.0.1"
The JAVA_Home is still: "C:\Program Files\Java\jdk1.6.0_25"
Given that Eclipse and Java run on Linux, Windows XP, and the Mac, and that Eclipse seems to run at good speed, thi seems like the best alternative for writing GUIs that let on interact with the Arduino-resident software.