If the transfer paper gets used upside down and the sticky part gets on the
top part of the press, what can I use to clean it off. I used a clean
cloth, heated the press, and pressed it onto the cloth. Much of the sticky
stuff came off on the cloth, but there is still some residue. Is there
something else I need to do to remove it, or should I just keep heating and
pressing?

Try using 409 or something similar with a non abrasive pad. That should get
it all cleaned up.