In my experience, you are on the right track...but you must be as consistent as possible. A couple broken arms on those who violate your wishes with your dog, perhaps...no, of course not...I am only kidding. !
Seriously, I have trained most of my dogs to NOT eat anything...even their own food...until given permission. The cue words I use are "All Yours". Done again and again and again, and with EVERY bowlful of food and every treat EXCEPT for training sessions, and eventually your dog should fully comprehend what you want and comply.
I trained my large dogs this way particularly because I had young children...at doggie lick bite level...and I didn't want any contests between my boys and my dog over their food. After a few years of her "SITting" while her food was put down, "STAYing" while I put away the food container, some petties and lovies, and then the "All Yours" command with visual cue toward the food, and when a child would drop something on the floor during dinner, she would not touch it at all. Once, it was a hot dog, and she LOVED hot dogs...Honey danced around me, and did her best to lead me to the hot dog...which she eventually successfully did...so I would give her the command to allow her to eat the treat. I also would tell her to "Stop" and pick up her food, giving it back to her a few seconds later with a second "All Yours" command. I didn't want a child to reach for her plate and have her become possessive...I wanted her to understand the removal of food was a temporary condition.
When I got two additional Shepherd/Labrador mixes, I had to re-train Honey because she wanted to react to every command...so I went with the puppies name followed immediately by the command.
I also used "Leave It" and "No"...all of which worked really well. Once, another dog we had was given an "All Yours" command and Honey was 'itching' to snatch the little feral kitty who had adopted us. When she heard "All Yours" you could see the "Do you mean it?" look of incredulity on her face and muscle tensing in preparation for 'the chase'...followed by immediate dejection after her "Honey, No" command. But, for that brief second, she could almost 'taste' that 'kitty crunchie' !
My first Yorkie...a Yorkie-Poo...was extremely well trained, too. He 'could' stand up and reach the coffee table, but his training included NOT raising his head above the edge of the coffee table. Food was always safe on the table.
A third training I have done with some former dogs is a "guard it" command...including food. I did it with three dogs, each guarding the food from all the other dogs. Training with the "guard it" command, I never allowed the food to be touched except by human hands, and they were never given the food as a reward for the behavior either.
I am not suggesting you try any of these options. Quite the contrary. I think you have already done a stellar job, considering the circumstances presented to you.
Keep up the good work...the reward is will worth it.
- Cat