Goof-off would take a lot of elbow grease, and a lot of goof-off, it is mainly for removal of minor latex, crayon, gum etc. Peel away will remove all the way to the metal, which is what I would do, both can be purchased at paint stores.
Use the peel away or stripper of choice (I use Bix)according to directions, useing plastic putty knifes, sand the bare metal lightly with a 220 grit, remove dust, reprime with a metal primer, sand lightly and remove dust, and paint, being sure to use exterior on the outside and a quality paint from a pro paint store (and I personally would recomend an oil paint, but either will work).
Now, some pre-primed metal doors come with a primer that is to be used for oil based paints only, it will say if you want to paint with latex you must first reprime with an oil based primer before painting with latex.
I have painted bare metal door jams that had an oil coating on them, and even bare metal doors and I had to clean thoroughly, I think maybe that was what the paint rep could have been thinking, I have never seen pre-primed doors with an oil coating, it would soak into the primer