Friday Matt took Doc to the vet, who gave Doc a physical exam, including especially checking his throat and his stomach, and the vet thought, as we had assumed, that Doc must have swallowed something. But Doc was happy and wagging his tale and showed no negative symptoms (other than the hacking) so the vet figured it would pass in time. In the meantime, he gave us this little word of wisdom...
Tip 37: When you have a dog with a stomach ache, feed it one cup of cooked rice, because rice will still give the dog essential nutrients, but it will not further upset the dog's already upset stomach.
We should add to this: After you cook the rice, let it sit for about 15 minutes to cool. We did not do so, and the rice was too hot for Doc at first, but he still was determined to eat it quickly no matter what.
The rice started out in the bowl, but it quickly made its way to the wall, and the rug, and Doc's paws.
The rice solution has worked well, and only 24 hours after his visit to the vet Doc is doing just fine. I am still going to guess that Matt and I will have the pleasure of being woken up in the middle of the night tonight when something like a bottle cap or a sock or a child's toy comes out of Doc's mouth, but for now things are fine, and the rice did its job.