Quite frankly, I’d take a different approach altogether.
Do you running if you must, but at least vary speed, distance and duration every time you run. Better yet, vary speed and running technique (forefoot running, standard running, sprints, backward running,…) a couple of times during each run. But then nothing beats HIIT when it comes to fat loss - if you have the guts. Also, this will get you into better shape than long distance running.
You can’t really do HIIT 4 days a week if you’re doing it right, anyway, so why not do long-distance (since you seem to want to do that) for 2 days and HIIT for another 2? You’ll be in a caloric deficit (quite so, at 2000), so that’ll probably burn you out already. If so, reduce on your long distance running.
To maintain lean mass, lift heavy. The meatheads will kill me for that, but as a matter of fact you don’t need to spend more than one day a week at the gym for maintenance, since you’ll be losing muscle during a cutting phase no matter what. 5/3/1 might work, but limit your gym time to a level you can keep up in a deprived state.
Also, how about supplements? Anything to speed up the process?
A thermogenic agent will help, as will consuming loads of green tea/coffee/water. You might want to stay clear of creatine for the time being to avoid subcutaneous water build-up.
Well, hope that helps a bit, even it went to a different direction.