There is the one about the time he told Pablo Escobar, ruthless kingpin of the Medellin cartel for which Munday worked, that he thought he was "stupid" - and survived.
Then there is the story of how he gave US Coast Guards a tow back to port using one of his smuggling boats after their own vessel broke down off the coast of Florida, secretly gloating to himself about the $300,000 worth of cocaine he had stashed in the front console.
There are tales of suitcases full of cash, drugs pick-ups in the Colombian jungle, night-time drops in Florida's Everglades swamplands, the night one of his aircraft was mistaken for a UFO over the Bahamas and the day he brazenly took a tourist tour of the White House while on the FBI and CIA's 'wanted' lists.
Now Munday, 67, who was part of the trafficking ring that in turned 1980s Miami into the most violent city since Prohibition-era Chicago - inspiring the television series Miami Vice and the movie Scarface - is committing some of his memories to record.
Philip Michael Thomas and Don Johnson in Miami Vice (Rex Features)
The last standing member of the so-called "Cocaine Cowboys" just recorded a spoken-word album of his memories, sharing some of the extraordinary tales from his six years as a drugs-runner for Escobar - a career that ultimately landed him behind bars for much of the 1990s.
"When I was doing what I was doing, then I was a ghost - nobody knows me, nobody sees me," he told The Sunday Telegraph. "But now people come to me all the time for stories. I served my time, the world's moved on, so why not? I guess you could say I'm a raconteur of history."
Munday earned up to $2.5 million a flight running drugs between Colombia and Florida from 1980 to 1986, a period in which the Medellin cartel trafficked an estimated $38 billion worth of cocaine. With him in charge of transport operations, working under Escobar's Miami point-man Max Mermelstein, the cartel became a powerhouse that accounted for 80 per cent of the US cocaine market.
As the drugs poured in, the streets of Miami exploded with violent turf wars - a bloody era that took so many lives that the city morgue could not keep pace with processing the bodies.
A maverick who taught himself to fly and never even held a pilot's licence, Munday's task was to literally fly under the radar, evading the combined might of US law enforcement agencies with methods so resourceful that his paymasters later nicknamed him "MacGyver" after the fictitious television secret agent.
The US government's eventual indictment against him spoke of the Munday Organisation's development and use of "sophisticated electronic equipment" to monitor and eavesdrop on law enforcement, remote-controlled electronic beacons that were placed with drugs to guide pick-up boats to their location, night-vision goggles, radar detectors, infra-red devices and radios that scrambled communications.
Yet one of Munday's favourite stories is of the time that he outwitted a US Customs patrol over Florida by simply flying too slow for them to catch him.
"My plane can do like 200mph and theirs about 500mph. So I can't out-run them, but I can out-slow them - they can't go slower than 120mph but I can get right down to 85mph," he explains.
"It hadn't occurred to them that high-tech doesn't always win you the game."
Munday has also now become an occasional resource for the US Military's Southern Command. Through SOUTHCOM's research partnership with Florida International University, he has twice been invited to speak to members of crime-fighting agencies such as the Drug Enforcement Administration, the FBI, Immigration and Customs Enforcement, Coast Guard, police and armed forces, to share information that could assist in counter-narcotics and counter-terrorism strategies.
"I don't mind helping. If I could bring in 1,000 pounds of cocaine at a time to make people happy, what's to say I couldn't bring in 1,000 pounds of something that could really hurt them? he says. "I've never made fun of law enforcement, they were never my enemy. I just took advantage of some of their weaknesses."
The story of Miami's 1980s drug war and its chief protagonists was the subject of a 2006 docu-film, Cocaine Cowboys, directed by Billy Corben.
Those on whom it focused are either jailed or dead - except Munday. The last to fall was Griselda Blanco, the so-called Godmother of the Colombian narcotics trade, who was killed in a drive-by shooting by motorbike assassins in Medellin last September.
Munday met the late Pablo Escobar a handful of times in Panama and Colombia to discuss operations, speaking his mind to the ruthless druglord despite his fearsome reputation. That included once calling Escobar "stupid" during a discussion about the poor state of some of the cartel's secret airstrips in Colombia.
"Immediately three or four guys got up and left the room, as if 'Uh-oh, let's get out of here.' This of course was a guy who, if he didn't like someone, would just order them killed. But to me he was just a businessman," says Munday. "My impression of the man actually wasn't that he was stupid. He was very intelligent, and he was polite enough to sit there and listen."
Nearly two tons of Colombian cocaine worth an estimated $175 million was seized from a warehouse at the Miami International Airport by U.S. Customs and Drug Enforcement agents, March 9, 1982 (AP)
Munday likes to separate himself from the stories of violence that punctuated the cartel's operations. He was "just the transport guy", responsible for getting the goods from A to B.
"I didn't buy it, didn't sell it, didn't use it, didn't steal it," he insists.
"All that violence? I don't understand it. I never did. I never even had a gun. Was I ever worried for myself? Nah. I was the goose that laid the golden egg, I was the one making them money."
While his cocaine cohorts cruised Miami in Lamborghinis and Ferraris, Munday largely eschewed the flashy lifestyle that his tens of millions of dollars in fees could have bought him, figuring that it was better not to draw attention to himself.
He channelled most of his cash into buying property, which was all forfeited after he was prosecuted. He now lives what he admits is a "frugal existence" in Miami, getting around on a pedal bicycle with his fashion-defying long, blond hair flowing behind him, his look perhaps more Dog the Bounty Hunter than Miami Vice.
He warns schoolchildren and students against drugs, yet retains a nonchalance about his one-time role in the cocaine trade, reasoning that the people who used it in the 1980s were largely the well-to-do seeking a good time and that he was servicing a need.
"Yes, I probably hurt people by bringing it in," he concedes when pushed. "That wasn't my intention."