Deadlifts and chinups are not close enough that one could be a substitute for the other.
Why is keeping your heartrate "elevated" for 30-60 minutes in your plan? What is that doing for you? No, really, what are you trying to accomplish from that? If your heartrate gets "elevated" to the point you can't hold a conversation while running, you are getting into anaerobic exercise, and you are just defeating your strength/muscle gains. And it's a waste of time. It doesn't give you the fat-burning of walking and slow running, nor does it give you the hormonal stimulus of a full-out sprint. That middle-distance, middle-speed stuff isn't helping you like you think it is.
Therefore, walk, or jog very very slowly. This will burn fat without stressing your muscles. (Lifting and sprinting is for stressing muscles.)
I don't know about Combat Conditioning, but Convict Conditioning is AWESOME if you want to spend the money. PB Fitness is conceptually very similar to CC, but doesn't go to as high of a level on the different exercises. (PB Fitness explains a lot more about the importance of walking and sprinting, but doesn't bother with one-arm pushups or pullups.)
Edit: Don't push your abs out. Don't suck them in. Brace them. It's different.