Funnily, the EXACT way other coaches and I usually go about getting really overweight and obese people is not right away through intense exercise or crazy calorie deficits. It's through increase in their daily physical activity.

Yes, you said it right, dropping food intake too much and increasing activity too much cause metabolic damage which is counterproductive.

That's why the key is to get a raise in their NEAT and their BMR. Being active not only burns calories but also increases your metabolism among other things.

Also, just this method works really well. I coached a college friend of mine and he DIDN'T diet or start hitting the gym. All I instructed him to do was - track his steps, move around more, and be more mindful of what he was eating. That's all!