Problem solved. Session matched, login working, now I just need to make it clean up after itself, wiping sessions as logouts occur. NBD.
A quick jump to the MySQL doc site was all it took to clear up what the delete syntax had to be. I honestly hadn't been able to delete anything from a table since I started this thing; the Perl For Sysadmin 15-minute SQL tutorial gives a syntax that doesn't include the word FROM, but when I tried it without the word from, MySQL always balked, every time. With FROM, it works. Again, problem solved. Being able to hand this thing in today is looking more possible than ever.
If I weren't worried about trademark infringement, I'd make a statement to the effect that I am "ssssssssmokIN'!"