Mansions, reticulan outposts, gov't ordinators/cruisers, raider gunships/fighters, hoppers, excavators, couriers, freighters, light gunboats, military transports, scouts, runabouts, and cutters all possibly have enemies with military shotguns. The freighters and couriers are probably your best bet, though excavator (resource extraction) missions tend to have plenty of chances to catch them on the ground.
That being said, if you can get the Kustom Blunderbuss, you're not far from shotguns and slug guns that outclass the military shotgun, so don't worry too much about not having military shotguns.