This is a long shot, but it's worked for me in the past. You could boot up a rescue disk, or a live-cd, and mount the root partition in read-write mode, navigate to /etc and open the passwd files in that directory with a text editor. Find the root line, which looks something like the following and is usually the first line in the file:
Delete the second field, that is in this example, delete the "x" and write the file. The field holds the password. Do nothing else in the file. Repeat for all the passwd files such as: passwd- and passwd.org if they exist. Then unmount the root partition, and poweroff and reboot on a powercycle. On rebooting, boot to single user mode as you mentioned in your post #4 above. You should be able to login to root without a password, just hit enter and if you are lucky you'll get a shell prompt that you can use. Then you can create a new password if you wish. This procedure can be used for a user as well. If it works for root though, root can create a user's new password.
Another idea occurred to me in relation to "protective software" misbehaving. You might consider disabling apparmor or selinux if either of those are running on your machine. You can do that by adding: apparmor=0, or selinux=0, to the kernel boot line which you can access through the grub menu after you hit "e" when the grub menu appears, navigate down to the linux line, add the relevant disabling option after a space and inside the quote marks and hit cntl+x to boot. You could try this procedure first and it if wasn't successful, I would consider doing this in addition to the first proposal above on your reboot. Trial and error.
I note that if this password issue was happening in single user mode at the terminal, it's not likely to be an .Xauthority issue.