I just thought of something the other day when my Dad's dog was incessantly begging for treats. I bet she wouldn't be on such a frequent treat regimen if the treats were chewy like gum, 'cause she'd be too busy chewing away on it to drop it, come back and ask for more... Reason being most dogs don't possess hording instincts like humans and squirrels do. They're content when they get just one of what they ask for and don't ask for more until the last bit they were given is gone. Dogs do not plan ahead… it's just not their nature.
So, I reckon dog gum could very well keep a mutt occupied with an endorphin-releasing culinary experience for a good 5-10 minutes at the very least. I'd give a dog gum all the time if it worked. Do you know how awesome it would be watching a dog walk around the house chewing gum? There'd be the annoying dog chewing noise to put up with, but the amusement of watching it chewing gum would far outweigh the audible mess that would ensue.
I'm going to the library tonight to find a good gum recipe and then Cub Foods to get the ingredients. Hopefully Schilling makes Imitation Liver Extract, for I'm planning on dumping just enough of that in to make dogs think Hey, this was specifically engineered for dogs and I'm going to chew on and savor this treat for quite some time because it's quite delicious.