Doing a lot of pullups won't really burn any more calories than doing fewer but heavier pullups. It's all relative.
If you want to burn off fat you have to eat less than your caloric maintenance levels -- meaning you have to eat less than what your body needs to maintain its weight. Now, you say you're willing to lose some muscle. Try your best to hold onto it because that muscle is what's going to help you burn the fat. I'm not going to go into details about cutting because (a) it's too complicated for me sum up now and (b) I'm not cutting until May (my first time), so I don't feel I'm experienced enough to inform you. You can check out cutting guidelines in the nutrition section.
However, some general rules for a cut: (1) lift at high intensity (i.e. heavy) and low volume (i.e. reps and sets). What this will do is give your muscles the stimulation to stay strong and large while your body is in an otherwise depleted (sort of) state. Don't go for high reps. So many people think while losing far that this will "shape" their muscles, but the only thing helping with that is pretty much genetics. Definition will come with a low body fat percentage. (2) Don't overdo the cardio, or, even better, cut it out all together. When on a cut, (assuming you have enough mass and your diet is adjusted properly) the change in calories/nutrients is all the body needs. Remember, if you drop weight too quickly you're very likely to lose muscle. (3) Cut down on the carbs, not necessarily fat. You need fat for energy and a lot of your hormone production. Also, believe it not, fat isn't really what makes people fat; only about 20% of our body fat comes from "fats" (and that would likely come from the trans fat culprit, and the much lesser evil, but still needed, saturated fat). Cut your carbs down to see a drop in body fat. But, make sure to incorporate refeeds. You'll read about these in the nutrition section. (4) Compound movements not only work MORE muscles but they burn MORE calories. Ditch your shrugs and preacher curls, and squat and deadlift some heavy iron. This is where your pullups are helpful. They happen to be one of the "big four" lifts of bodybulding (pullups, bench press, squats, deadlifts). You can work every muscle in the body with these, and very effectively, I might add. (5.) Focus on control and consistency. This isn't a time to bring in new, unusual lifts or programs. Stick to the basics and lift mindfully.
Hope that helps. Maybe talk to Built. She knows.....