engage in heavy weight training sticking to lower reps, nothing above 8 reps, mostly 4-6 reps per set.
the cardio HR thing is misleading. the 'fat loss' zone, is really the minimum heart rate you need to be doing aerobic exercise. typcially in fat loss you're burning 50% of your calories from stored fat. As you work harder, the percentage drops to 40%...however you burn a lot more total calories, so the net calories burned is higher, and 40% of 300cals is more fat than 50% of 200 cals.
ideally in cardio, at least in my opinion, you're best of doing intervals...work really hard a couple mins then taper off, catch you're breath, then burst again. you can get a better workout, more cals burned, in less time than a slower pace.