the good post:
1) Cardio: Have you ever tried lifting weights without employing your heart and lungs? With a well structure routine ie supersets, minimal rests, high intsnity (thats weights not speed and is relative to the ibidvidual) your heart rate will stay elevated for a longer period.
2) calorie burn: Dont use exercise to create your calorie deficit, there are way too many variables, how you feel on the day, how well you worked out, how consistant you were, how much sleep you got the night before, how well hydrated you were the list goes on.
IT TAKES % SECONDS NOT EAT 500 CALORIES AND UP TO AN HOUR TO BURN THE EQUIVELANT.
So use the gym to maintain muscle mass and the kitchen to burn the fat. Its far more easier its more sustainable and gets consistent results hand over fist.
Now the big but, and we've all had one of them :-) , if running is what it takes to keep you motivated to lose weight then that is the best approach as it is with any approach. From your post I dont get that impression. The most important thig though is to understand how the body works and that training can not be taken into isolation.
If you decide to run, your calorie intake needs to reflect that. If you want to burn calories then you need to be in deficit ie below your basal metabollic rate, there are loads of calculators on that. Too low and the body starts to conserve and teh metabolism slows