Losing muscle when losing fat is a fact of losing weight, ask any body builder. Now the slower you lose it, the higher percentage of muscle you can hang onto, but you will still lose some.
@North Coast Miller is right. Look to sumo wrestlers on how to gain body fat and lots of it, eat and then sleep. If you want to lose, go to bed hungry, gain, go to bed full or take a nap after eating.
You have to eat for what you plan on doing the 4 to 8 hours after you eat. Also going for a walk after dinner helps lower blood sugar levels.
Now I'm going to rock the boat here and say yes, it is possible to out work a "bad" diet, just ask anyone that put up hay, shoveled snow or pulled green chain. Or ask anyone that walks for 6 to 8 hours a day. One hour of walking burns about 600 calories (depending on a few factors), now make that 6 hours of walking and you burn a whopping 3600 calories. In fact if you don't eat enough, you will bonk out.
The main problems with this approach is most people don't have that much time and people have a tendency to up the intensity too much and make it more glycolytic, which will turn you into a raving lunatic when it comes to food.
If you try to cut back food, your training is going to suffer, work more on timing what you eat.