I thought residents of on-base hosing (no, that's not a typo) are allowed to keep firearms in their residence as long as they're registered with Security Forces? Check whatever base you are going to for it's policy.
If you have to leave a weapon in the armory (never a good idea but may be the only option), put your own trigger lock on it. In fact, since only the receiver is technically the "firearm," consider removing the upper (if an AR) or other internals (if any other type of rifle) or barrel if a pistol. Nothing says you cannot keep gun parts in your residence, just complete firearms!