My ex-husband was a chemist. His recommendation was always acetone (nail polish remover) and a cotton ball. I know it works great on getting off the sticky residue that labels leave behind. I would imagine it would work on the plate of your iron.
I just removed a repair label a business put on my sewing machine over 20 years ago. I first tried Goo-Be-Gone and it didn't do anything. I then got my nail polish remover and off the sticky came.
The thing is, your nail polish remover must be acetone, not a synthetic.