The problem was simple (once I got the installation documentation)

My Zif programmer is screwed down to a board, so I couldn't turn it around. NOW, I know what was happening and why.

I didn't just put my chip in a different direction, I had to turn aroud the Zif programmer and move the cable connector to the other side as well. So my school gave me a new programmer that was't screwed down so I could do that. It was simple, so I feel silly but all ends well.