I called the vet and we got Toby and appointment for tomorrow at 2:30. The vet said that he'd probably pass it, but to bring him in anyway. We decided to try an experiment, so we put the other piece of ribbon in front of him to see what he'd do, and he chomped right down on it like it was a piece of candy. The good thing is he bit right through it, so I guess there's a chance that he actually chewed up the other piece rather than swallowing it whole.
I'd imagine that your pig chewed it up before swallowing it. I can't imagine he'd swallow 18 inches whole, y'know? But I suppose weirder things have happened.