We do the same thing…leaving the two Scotties staring at each other in sadness! Actually they get the second-hand gnawing time.
Janet used to have hard time keeping a straight face when we were at one of our favorite places in SoCal. We both would order the King-Cut size on the ‘Prime Rib’ menu. That would be cut full-width of the bone-in slice. Janet could Never finish hers, and I would do as you mentioned, leave a wide border along the full rib bone. Then it would be ‘Doggie bag’ time. Home we go to our own ‘gnawing session’…Then Wolfus, the Wonder Dog" and Boomer, The outdoor Guard Dog would get second ‘dibs on what was left after we finished. Now that we have the Scotties here in Indiana, they tend to be more assertive about our sharing the remains from the Doggie bags.