Consider this as a possibility:
Go to the Java web site instead of crawling around on Oracle's site.
Then select "See all downloads"
Find the "Java 6 Download Page" link.
This version has now been added to the normal jdk6 previous version downloads page: http://www.oracle.com/technetwork/java/javasebusiness/downloads/java-archive-downloads-javase6-419409.html
Thanks to everyone who looked into this!