It was 5 p.m., and Eddie Jabbour knew that taking the subway would be faster than dealing with traffic. Cars would be backed up all the way from his office near the Empire State Building to the SoHo restaurant where he was taking an out-of-town client. But as the two descended the subway steps, his client confessed that he has always been intimidated by New York’s subway system.

“It’s a labyrinth,” Mr. Jabbour agreed. “It’s just a hole in the ground, and the hole is a maze.”

After they boarded the train, Mr. Jabbour tried to locate their route on the map inside the subway car. “That’s when it came to me,” he said. “It’s the map! The map is the last vestige of the old system. If you can’t read the map, you can’t use the subway.”

Since that day nearly five years ago, Mr. Jabbour, a 54-year-old co-owner of a marketing company, has devoted his weekends and evenings to studying old transit maps in an effort to produce one of his own. Persuading the city to adopt his new map, which he says is more stylized than the current map and therefore more accessible to non-New Yorkers, has become something of an obsession.

“The map is an icon of the city; it represents New York on a certain level,” said Mr. Jabbour, a small, restless man who was born in Bay Ridge, Brooklyn, and lives in Hastings-on-Hudson in Westchester County. “And it takes a cryptic archaeologist to read this one. It’s like the Rosetta Stone.”

A self-proclaimed “subway foamer,” or buff, Mr. Jabbour has a passion for transit-related subjects like infrastructure, routes and track design.

“It’s definitely his passion,” his 17-year-old daughter, Ellie, said of his map, adding that nearly every weekend he prints out a new version and asks her opinion on alterations she has trouble even seeing, like “slight modulations in subway line thicknesses or color changes.”

The other day, in his minimalist office, Mr. Jabbour pinned two maps to the wall, ...