I added 1/2 cup orange juice to the chopped oranges, secured the food processor lid, and flipped the machine on. OJ went everywhere! I still have no idea what happened. So I added 1/3 the juice of an additional orange, poured the puree into a bowl and abandoned the food processor. I was supposed to mix in the butter using the machine, but since I now needed to hand-mix everything, I microwaved the butter until softened. The batter came together quickly and easily, and it had a surprisingly airy consistency. It was similar to the consistency of whipped cream but thicker, and when I ran a spoon through it I could hear air bubbles breaking. I was curious to see how the muffins would emerge from the oven.
They turned out just right, thanks to my keen sense of smell. After about 10 minuted they began to smell done, and they looked ready to come out but they wouldn't spring back when poked. But at the 12 minute mark they were ready. A full 8 minutes less than prescribed by the recipe!
But as I said, the muffins were good. They were composed of a very tender sponge with tiny toothsome pieces of orange flesh. The orange flavor was light but distinct; it was nothing like fake orange flavor, and not even very reminiscent of the fruit, but clearly "orange." To be honest, it was disconcertingly similar to the flavor of orange Hostess cupcakes that I remember from my childhood. I'd make these again if I needed muffins to serve guests but didn't have the ingredients for blueberry or banana nut muffins. They were quick and fairly tasty and stored well for several days when sealed in a container at room temperature.