Yes, caloric cycling is how you'll likely have the best luck losing the body fat, but it's a little more complicated than just cycling calories.
Pick two days that you schedule your lift heavy things workouts and put them back to back. For argument's sake, say you'll put deadlifts, benchpresses, lat pulldowns, shoulder presses and bent over rows on Saturday and squats, leg presses, leg extensions, tricep pulldowns, bicep straight bar curls and crunches Sunday. The rest of the week, you do the easier stuff. HIIT on Monday, light weight depletion weight work on Tuesday, light weight depletion work on Wednesday, low level cardio on Thursday and off on Friday.
Monday through Friday, eat at a caloric deficit of around 20-25%. If your maintenance is around 1,800 kcal, eat around 1,400 kcal. Keep carbs under 50g, no starch, eat 1g of protein per pound of body weight and whatever's left eat fat, preferably MCT-based fats like coconut and butter.
Saturday and Sunday, eat 20-25% over maintenance. That means around 2,200 kcal. Those days, eat 1-1.5g/lb of body weight of protein, 200-250g of starchy carbohydrate (skip the fibrous veggies) and keep fats low, under 50g total.
That sample plan will probably get you to where you want to be in 4-6 weeks. Just plug in your maintenance calorie level (body weight in pounds x 14 roughly or use an online calculator). Of course, before you embark on that diet, take a deload week. Don't do any kind of heavy training. Maybe some walking, pushups or crunches, but nothing that'll make you sore or tired. Eat at maintenance calories or a little more so you reset your metabolism.
I'm in the middle of something similar now, except more extreme.
P.S. I like the username. Witty.