Hello and welcome to the forum. It sounds as if your original choice of food was the better one. You have identified the reason why your dog is putting on weight so that's a good start. If he was doing well on the high meat content, grain free food then it makes sense to to go back to it. When dieting a dog, I find that it is important to weigh the food accurately. If the dog is weighed weekly it is easy to see whether he is losing weight and if not, reduce the amount by 10%. It's not unusual to have to feed less of some of the higher quality foods and the amount needed does not always reflect the recommended daily allowance.
Re the treats - you can take some of the kibble out of the daily allowance to give as treats. There are low calorie treats such as sea jerky. Dehydrated chicken strips might also be useful. Be sparing with your treats and don't feed the dog from the table. If he is a scrounger, put him in another room while you eat and then you won't be tempted to feed him.
Re grain free food being better than grain containing ones - it depends on the ingredients. Some grain free foods rely on white potato
and pea flour
for the starch which is necessary to form the biscuit. Some grains are useful nutritionally, particularly brown rice.
The other thing to consider is the question of quantity. The better products contain more meat, vegetables and botanicals and less starch.
Hunger - some dogs are naturally greedy and we often mistake this for hunger. It can be a behaviour problem more than hunger and the fact that your dog is used to treats seems to confirm this. You need to be firmer with him. Check his weight weekly until he gets to the right level and have a look on YouTube for videos about body condition scoring. This is a really useful way of assessing the dog's healthy weight. Weigh his daily allowance of food and put one or two acceptable treats in a pot. He gets nothing else but you may need to get the family on board with this because it's no use you sticking to the rules if someone else is continuing to feed the dog. Cooked, mashed suitable vegetables can help to bulk up the food a little and they have nutritional value but don't pick the starchy vegetables.