we have tried goo-be-gone, vinegar, bleach, toilet cleaner, laundry soap, rubbing alcohol, and baking soda
Use it as an excuse to re-decorate. Cause you are gonna have to paint over that mess.
Try a Magic Eraser. Follow the instructions that come with it.
Metal or painted metal? If it's bare metal, try acetone (nail polish remover). If it's painted, you could still try acetone, but on a hidden spot if you care that it might mar the paint. Beyond that, a mild abrasive like automotive rubbing compound or maybe work your way up from a polishing type auto wax.
Rubbing alcohol does a good job at removing permanent marker off metal and plastic surfaces.
This is what we do at school to remove permanent marker from the white boards. It has also worked on regular chalkboards. Some teachers make the mistake of picking up the wrong marker, or picking it up instead of chalk! Get a marker for white boards. Trace over the permanent marker on your door and wipe it off immediately with paper towel or a cloth. If there's a lot, do it in small patches because even that marker will dry. It's not permanent, but you'll be adding extra work.
