Interesting because in my case, works only method mentioned by WIN98SE (of course I have disabled next generation Java-plugin).
In fact, I haven't tried to install new version over previous one.
Btw, it's good to hear, that latest Java works with Firefox 3.6.8 (Moziila will end soon supporting Firefox 3.5.x).
It is really a bug of the new Java 6.21. It does not unregister the NextGenPlugin for Mozilla-Browsers correctly.
I tested it with Seamonkey 1.1.19 and Firefox 3.5.11
Maybe EvanD's NextGenPlugin was already "unregistered" before the update to 6.21.
I really do not have a clue how to unregister a Mozilla-plugin.
But I do not believe that Java works with Firefox 3.6.8.
I thought Firefox 3.6.8 only works with the NextGenJavaPlugin.
I tested it with http://pluginchecker.com/