Thanks to Michelle Tam (Nom Nom Paleo), I've discovered the goodness that is Eggs in Purgatory. She graciously shares her recipe here:
Uova in Purgatorio
How did I not know about these before? I substituted ground beef plus my seasonings for homemade sausage for the Italian pork sausage. Also, since I was testing it out just for myself, I made the whole thing except for the egg, then ladled some of the meat sauce into a microwave safe mug. I cracked an egg into that, covered it with a microwave-safe plate, then zapped it for 2 minutes on 50% power (cook until the egg is done to your preference).
The test was successful. I am now motivated to buy ramekins.