You handle that by keeping the same ammo and gradually phase in the new rifle!!!
With the terrorists actually outnumbering the enemies we faced in WWII, I must agree. (1.5 Billion Muslims X 15% ready to rumble on world-wide jihad). The "Moderate Muslim" argument makes about as much sense as the "Good Germans" argument in WWII! The "Moderate Muslim" supports the jihad just as much as a "Good German" working in the Krupp Works, or buying German War Bonds.
But when it comes to weapons, our procurement people seem just as hide-bound as the stodgiest Civil War thinkers, who stuck with muzzle-loaders when the 7-shot Spencer Rifle was readily available. Our Pentagoners are stuck on 5.56.