I received loads and loads of advice in the comment section of that post, for which I am very grateful, and this Sunday evening it took me just about 30 minutes of work to git-r-done.
Here's the "before" picture:
First, I gathered my tools (sponge, bowl of warm water, and a plastic knife from a take-out restaurant):
After a few minutes of gentle pulling and pouring of some warm water over the magnet, it looked like this:
And that's the spectral apparition known as the Ghost of HansDat in the reflection.
Then, I alternated prying/pushing with the serrated blade of the take-out knife placed nearly flat along the edge of the door/magnet area along with pouring more warm water over, and then gently pulling the magnet. This painstaking work took about 15 minutes and at least three bowls of warm water, but finally, VOILA!
Those little white marks are hunks of the white-washed magnet decal, and there are a few flecks of the brown part of the magnet there, too, but I managed NOT to chip any of the paint.
It looked like this the next day...
So, just a few flecks and that helmet outline are all that remain of my error. Not too bad, I say!