It’s possible that your training is getting in the way of weight loss. I’m a true believer that you should eat for your goals. It sounds like your goal right now is the Ragnar Relay. Getting your body ready for that AND losing weight might be a challenge. This is especially true with the amount of training you’re doing right now. Your body may not want to give up that stored energy source if you’ve been pushing it to its limits on a weekly basis.
So, should you enlist in the military diet? Well, seeing as you've made it this far, you've (hopefully) realised that the plan has no legs. Yes, a caloric deficit will bring about weightloss in anyone — regardless of gender, age or dietary preferences — but the safest option is to do it moderately. Culling your intake by almost 1000kcal on the military diet will be harming your body more than it's helping it, so instead look to drop 200kcal a day to lose weight gradually and safely.