I believe you that the won't take you for your weight. I'm in the army currently, and have been for almost three years and guidelines have since become rules. At the moment, coincidentally, paperwork is being generated for my seperation from the army for a similiar reason. I weigh 215 at the moment fully hydrated (I can lose 10 lbs. in two days, easy. 4 mile runs+sauna+hot showers) and the standard for my 5'11" height is 195. We are allowed taping when we weigh over, but it is computed with a neck to waist ratio, which is probably the least accurate method of computing bodyfat ever discovered by man. I wear size 34 pants but because I was severely overweight when I was younger, I have love handles despite the fact that the rest of my body is lean. My neck is small, 15", and my waist comes in at 39", so according to them, I have 26% bodyfat.
I can do 73 pushups in two minutes, 90 situps, and I run a two-mile in 14:30. I have never been given a negative counseling or action, every Sgt. in my platoon has issued a request for my retention, and my profession requires 11 months of training and we are at only 71% strength as it is. By no act of common sense should I be discharged, but welcome to the military, my friend, where rules are unbreakable and physical standards of bodyfat apparently haven't changed in 30 years. Meanwhile, my friend who hasnt passed his physical test in over 9 months is fine, because he's thin and weak.
You got to deal with it, bro. Take your time and drop the weight healthily. Find a local gym that offers cross-fit classes. They'll drop that weight in a heartbeat.