Easy... simply create a directive forbidding the use of the unauthorized body armor, and threaten soldiers who use it with the loss of their benefits and with disciplinary action.
Let the soldiers wait around instead for the chance of getting ahold of the government-issued body armor... even if the military's own reports show that it's often inferior to the commercially-made products. Infact, it's so bad that its use might have already cost hundreds of lives.
It's not too comforting to know that the military's biggest supplier for their body armor is being sued by the government for knowingly manufacturing faulty bulletproof vests... and the other major supplier was forced by the Marines to recall over 23,000 Point Blank Interceptor vests because they failed, among other things, ballistic quality assurance tests.
Ah well. At least the companies with the contracts to make the military's body armor are well protected.