Well, the cat did not come back on his own, and it wasn’t the next day, but he has returned.
Thanks to the kindness of a nearby resident, my cat is once again dozing comfortably on my furniture, and the puppy is having to stay outside and give hime some much-needed space.
Burnie had apparently chosen to take up residence at Huffman Point, relying on the generous nature of some of the people there to feed him and even let him in at times.
Al Huffman had apparently seen one of the posters I had put up in the area and took note of the phone number.
The kind lady who had been feeding Burnie and taking him in, called and we were reunited (Though he has been taking periodic forays back over to visit, looking for company and food in both places now, I suppose).
I’m not sure he was super keen on going back to puppyville, but we are working on boundaries and he’s pretty content at the moment. I am carefully ensuring he gets his required amount of attention. Puppy is adjusting to her reduced indoor time.
I am so grateful for the kindness of those who helped bring Burnie back home.