I am trusting you with a mission that is risky and of maximum importance.
I'm not entirely certain how 1954's The Island Monster (or Il Mostro dell'isola as it's known in the original Italian) qualifies as a "Drive-In Movie Classic" apart from the presence of Boris Karloff in the cast, but I guess that's enough for some people. Co-written and directed by Roberto Montero (based on a story by Tickle Me Carlo Lombardo), the movie takes place on the Isle of Ischia off the coast of Naples, where mustachioed treasury agent Renato Vicario has been sent to smash an international drug smuggling ring. That covers The Island part, but there's no actual Monster unless you count Karloff, who poses as a philanthropist running a charity children's hospital, but is actually the smugglers' ringleader. Of course, it should be obvious he's up to no good since he spends most of the film in a Gilligan hat.
Actually, the real monsters are the ones who worked behind the scenes. Not just Montero, who pads scenes out mercilessly, but also whoever was responsible for the dubbing, which is positively atrocious (even Karloff sounds like he's dubbed by a guy doing a mediocre Karloff impression), and the sound editing, which is choppy even for a low-budget movie. The padding is what really saps the film of its energy, though. It's as if Montero had a "we shot this and we're going to use every single foot of it" mentality. Listen, that's fine for a rough assembly, Roberto, but haven't you ever heard of the concepts of pacing or tightening?