Interest Check: Monster of the Week
Here's what I was thinking, I set it in 1956 since it's the height of Eisenhower's America. It's also the year Godzilla debuted.
George Washington, being a high level Mason, knew of the Royal Cabal of Wizards kept by the Court of St. James. When the War for Independence broke out, he recruited experts in the supernatural amongst the colonists to covertly combat the British mages. Once the war was won, he incorporated the experts into the Concilium Invisium, the Secret Cabinet, as the New World was a sudden refuge for preternatural beings of every ilk from all over the world, much like the nascent population of America.
The Secret Cabinet continued it's fight against the supernatural for a century and a half. By the outbreak of World War II, the monsters and magic of America, much like the country itself, had been tamed. Everything changed on the fateful August day when the first atomic bomb was dropped. The resultant explosion seemed to roil magical energies, emboldening monsters and magecraft across the globe. To make things worse, in the ensuing years, Science has run amok, and the atom created a whole new breed of monster, mutated from terrestrial creatures exposed to radiation, and a new breed of mad 'wizard', who uses science instead of sorcery.
It is 1956. The Secret Cabinet is now know as Majestic 12. Its agents combat the things that go bump in the night, be they gigantic fire-breathing dinosaurs, mad scientists, or good old fashioned vampires, werewolves or witches.