When I used to hunt on military bases, there was a very set procedure in place to allow you to bring the firearm for hunting (and no other) onto the base.
There was a single gate that was used, manned by MPs and often with an officer present (even at 0500) to make sure you had the required permits including the base hunting permit, and that your name was present on the 'hunting access list.'
It was never a major hassle, just part and parcel of entering a restricted area for a specific purpose.
Many times the gate personnel appeared to be more interested in what we had seen when scouting previous days than anything else.
More than one base assigned hunting locations and supplied a map showing all the locations and emphasized only shooting in 'safe' directions from your assigned location.
Other bases assigned areas to each person and supplied detailed maps.