What has worked for me is to separate the concept of losing bodyfat vs increasing fitness.
The fastest way for me to lose bodyfat is to do super low carb and restrict physical activity to walking and gentle yoga. My energy level drops, but the pounds of fat just shed as long as I stay in ketosis.
When I try to get fitter, I hope to maintain bodyfat or accept a small increase.
As I get more savvy, I hope to mix the two - but for losing a solid 50 pounds of fat, the first approach is what worked. Doing yoga and getting more flexible made me feel that I was getting fitter in some dimensions, even as my strength and endurance waned during the long period when I was burning off the fat.