Still need to get this to work. I did everything in the fstab and all the stuff the beginning of this post. Get same results. Access denied to /mnt/zip after it gets mounted.

root@rrfish72:/# ll mnt/zip
total 4
-rwxr--r-- 1 root root 4079 Feb 15 1995 readme.txt
Access denied or not? Clearly you can list the files on the disk. Perhaps it's just that you mounted as root and tried to access as user. This is now when the line in fstab comes handy. Unmount first if it's mounted and then try mounting as user with mount /mnt/zip

How do I get at the readme.txt file to actually read it?
You mean like:
cat /mnt/zip/readme.txt
mcedit /mnt/zip/readme.txt
kwrite /mnt/zip/readme.txt

Actually I got to read it somehow. I just clicked on the icon and it was there. Now I can't get to it again.
If it's mounted by root, you probably can't access, but if it's unmouted, clicking the icon should mount as user and permit access.