I think you'd be better suited focusing on strength more at first. The effectiveness of any conditioning you do with complex training will be incumbent on your strength levels. So you postpone the fat-burning at this point a bit so that you can burn that much more, much quicker, once your strength is solid again. Quantitatively, I'm talking about the difference between winding yourself with just a 45lb barbell after 3 rounds v. dominating with 95lbs for 5 or 6 rounds.
Perhaps you could try something like lifting 3x/week, complexes 1/week. As you increase your work capacity again, add a second complex day. You can also add some morning walks to the mix at this point for an extra caloric deficit that won't promote catobolism.