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Emma Coronel, mother of Guzmán's twin 4-year-old daughters, has given unprecedented media interviews, issuing dire warnings about his health and pressuring the government to improve the conditions he endures his third time behind bars.
His lawyers have gathered the media at Mexico's supreme court and outside the White House in Washington.
On Friday, one of Guzmán's lawyers called a news conference outside the maximum-security Altiplano prison where he's being held - where he says the guards and security measures are turning him into a "zombie" - and which he escaped from through a mile-long tunnel in July.
Wearing an "Extradition Never!!!" sweatshirt emblazoned with a photo of his client, attorney Jose Luis Gonzalez Meza said he planned to begin a hunger strike - water and juice allowed. He called on Mexicans to join him.
'Grasping at straws'
Analysts say the publicity is all part of a carefully planned media strategy.
At the very least, Guzmán hopes to negotiate the terms of his imprisonment in the US, should moves to extradite him succeed.
Another Guzmán attorney, Jose Refugio Rodriguez, says that the drug lord wants to be sent to the US quickly and negotiate a guilty plea in exchange for a "reasonable" sentence in a medium-security prison in the US.
Samuel Logan of the business and security-consulting firm Southern Pulse said he doesn't believe the effort will work.
"El Chapo's folks are grasping at straws," he said. "I doubt the US will negotiate on any level."
The PR campaign has featured Guzmán's common-law wife, a former beauty queen, giving her first public interview ever in February.
Conservatively dressed and poised throughout her conversation with Telemundo, Coronel painted an image of "El Chapo" as a loving family man. She was careful to suggest his innocence, or at least not confirm his guilt.
"I'm not certain that he traffics drugs," she said.
Guzmán's American daughter has also defended her father, and implicated the Mexican government in his cartel's operations as well as her father's escape from prison last summer.
"My dad's escape was an agreement," she told Rory Carroll of The Guardian in an exclusive interview.
'I think people are just tired of having him around'
Guzmán's attorneys have publicly expressed concern for his health and criticized his treatment while jailed.
"How long is his body going to tolerate this state of stress that he's submitted to?" Rodriguez said last month after a 30-minute visit at Altiplano prison with Guzmán. "If this doesn't stop, he is going to get sick and his life is at great risk."
Outside the prison Friday, Bernarda Guzmán Loera, who said she was one of the drug lord's sisters, said his family was "very worried."
The drug lord's lawyers have filed several requests for injunctions in Mexican courts to stop his extradition. Rodriguez said Wednesday they won't drop those efforts until they get an agreement with US prosecutors, an unrealistic scenario.
Things were a lot different for Guzmán the last time he was in prison, after being captured the second time in 2014. Mexico's then-attorney general said the drug chieftain would only be extradited to the US "in 300 or 400 years" after serving his Mexican sentence.
REUTERS/Ginnette Riquelme
In a recent court filing shared by his lawyers, Guzmán described a relatively permissive environment with plenty of access by outside visitors and some freedom to move around.
"Half a year ago I was in this place and had a daily visit of an hour and a half with my
Raul Benitez, a security specialist who teaches political science at the National Autonomous University of Mexico, said during that earlier imprisonment authorities "did not violate his human rights, quite the opposite. They practically let him open an office in the prison to run his businesses."
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But then "El Chapo" pulled off a brazen escape, coolly stepping into a hole in the floor of his prison-cell shower and whizzing to freedom on a motorcycle modified to run on tracks laid the length of the tunnel.
President Enrique Pena Nieto was embarrassed by the escape in July, Guzmán's second from a maximum-security prison.
The first escape was in January 2001 from a prison in Jalisco state. After Guzmán was recaptured in January of this year, Pena Nieto said the drug lord would be extradited.
Now Guzmán's visits with his lawyer and his wife are shorter and chaperoned. Guzmán complains that frequent bed checks, barking dogs, and regular prison racket keep him from sleeping and drive his blood pressure to dangerous levels.
National Security Commissioner Renato Sales has denied Guzmán's claims that authorities are violating his rights.
"Shouldn't someone who twice escaped from maximum security prisons be subject to special security measures? The common sense answer is 'yes,'" Sales said.
Now, Logan said, "the politics are against him."
"Any backroom deals that he may have cut before are rendered null now that he escaped and embarrassed" Pena Nieto, he added. "He's a king in his own fiefdom in the interior of Sinaloa (state), but nationwide I think people are just tired of having him around."