The army lied to you about doing cardio on an empty stomach. If you have no fuel, you won't get an optimal workout. A true workout that's designed to burn fat isn't about how many calories you burn during the workout. It's about how many calories you burn as a residual effect.
If time is limited, you need it to be a highly intense workout. I also suggest getting some strength training. The more you build muscle, the more calories you'll burn while at rest. Fuel your workout with some carbs and protein, then hit it hard. Keep your metabolism active by eating smaller meals, throughout the day instead of just 2 or 3 large meals. Drink LOTS of water.
It's a myth of turning fat to muscle, which leads people to want to burn the fat BEFORE building the muscle. Building the muscle will HELP burn the fat. Anyway, if you want more info give me a holler. I don't want to throw too much at you at once.