I appreciate your being unhappy with the school restriction. Don't recommend you carry concealed into the school due to the hassle you will encounter if you are discovered. Lobby for a change in the law for licensed concealed-carry.
Heat won't be a problem per the ammunition if you rotate it out every four to six months. Just shoot up what's in your gun and replace with fresh ammo.
Hate to be the bringer of bad news, but that combo, if the gun can be fired from within the holster, is classified as an "AOW," or "Any Other Weapon," by BATF. As such it is subject to the NFA and must be registered. $200 tax stamp on a Form 1, or have a Class 2 manufacturer register it and pay the $5 tax stamp on a Form 4.