As it turns out, our garage door is not vinyl, but instead it is metal! This is very good news indeed.
Vistaprint can reproduce my artwork onto small car door magnets, about 8.5 X 11.5 inches. Occasionally they offer a custom magnet for free, plus shipping. Here is the beginning of my garage door art gallery with some of my artwork. Using magnets won't mar the door, and I can move them around when I want to.
How fun is this ?!?