Special Agent Geoff Kelly, the lead investigator for a decade, said agents had confirmed that one or more of the missing works was offered for sale here a dozen years ago.
"We don't know if the deal was ever consummated," Kelly said in an interview, "but we were able to corroborate the information that they were seen in Philadelphia - it appears to me, more than once."
Connecticut was also a destination, but investigators were shy with the details.
They said they suspected who the thieves are, but Richard DesLauriers, the special agent in charge of the FBI's Boston office, would describe them only as "members of a criminal organization with a base in the Mid-Atlantic states and New England."
One reason to stay tight-lipped: the statute of limitations has passed to prosecute the robbers. What the authorities care about is recovering some of the most valuable and famous art in the world.
Among the items stolen was The Concert (1658-60), one of only 36 known works by the 17th century Dutch master Vermeer. The oil painting depicts two women, one at a harpsichord, the other standing alongside, completely absorbed in their imminent recital.
Three Rembrandts were taken. They were two paintings - The Storm on the Sea of Galilee (1633), Rembrandt's only known seascape, and A Lady and Gentleman in Black (1633), a double portrait - and an etched self-portrait.
Landscape With an Obelisk (1638), an oil long thought to be by Rembrandt, was taken from its spot opposite The Concert. In the 1980s, scholars identified the artist as Govaert Flinck, a pupil of Rembrandt.
The Vermeer, the Rembrandts, and the Flinck were removed from the second floor of the museum. On the same floor, thieves helped themselves to five drawings from the 1880s by Degas, all on paper.
Manet's small oil Chez Tortoni (1878-80) was taken from the first floor, and thieves also stole two objects: a 19th century gilt bronze eagle from atop a pole supporting a Napoleonic flag and a Shang Dynasty bronze beaker from 1100-1200 B.C.
Kelly said the bureau decided on a public blitz because the investigation had "ramped up" in the last few years, and agents realized a few 21st century tools might help them finally solve a vexing 20th century case.
They unveiled a website with photos and videos of the artwork and investigators, and trumpeted a long-standing, $5 million reward from the museum.
Within three hours, the FBI web page on the case had been shared more than 500 times on Facebook and Twitter. Images of the stolen works will begin flashing on about two dozen digital billboards across the Philadelphia region, along with e-mail addresses and phone numbers for tipsters.
"I absolutely think we're getting close. We're hoping that this is going to push it over the edge," Kelly said. "Someone could be a millionaire and nobody has to go to jail."
Investigators have been close before.
Robert K. Wittman, a retired Philadelphia-based agent who spent a quarter of a century chasing stolen art, said he worked an undercover FBI investigation five years ago that tracked two stolen Gardner prints from Miami to a crime network in the south of France. In the end, Wittman said, the paintings and their then-owners got away.
"I don't think anybody is buying them and hanging them on the wall," said Wittman, who founded the FBI's Art Crime Team and now runs his own art security, consulting, and recovery firm in Chester Heights.
He said the missing paintings have probably passed hands a few times since then - if they're still around. The Gardner thieves sliced the paintings from their frames, which could hasten their deterioration.
Most often, such thieves are run-of-the-mill criminals who pull the heist and then sell the artwork across other crime networks, usually for a fraction of its worth, agents said. Years pass, and the cases break when someone tries to sell a stolen painting legally.
Though the statute of limitations on the thefts expired, owners could face charges related to possession of stolen artwork.
The top federal prosecutor in Boston suggested that her office might be willing to forgo such charges solely to retrieve the artwork. "Our primary goal is, and always has been, to have the paintings returned," said U.S. Attorney Carmen M. Ortiz.
Kelly said he did not understand why someone would keep the paintings, even why they stole them in the first place.
"You could say it was the perfect crime, but really, what did they get?" the agent said. "I don't think they made any money off it, nowhere near [what they were worth]. It probably would have been more profitable to steal and strip a car."
Contact John P. Martin at 215-925-2649, at firstname.lastname@example.org, or @JPMartinInky on Twitter.