Four imprisoned former New Orleans Police Department officers asked a federal judge Tuesday to release them on bail while they await a new trial on the 2005 shootings of six civilians on the Danziger Bridge and an alleged cover-up.

Kenneth Bowen, Robert Gisevius, Robert Faulcon and Anthony Villavaso appealed to U.S. District Judge Kurt Engelhardt to release them to see their children.

They claim holding them any longer would violate their due process rights, now that the federal government has all but depleted its appeals of Engelhardt’s 2013 ruling vacating their convictions and lengthy prison sentences.

All four men have remained behind bars for nearly six years, beginning with their surrender in mid-2010 following a 27-count indictment charging them with civil rights, firearms, conspiracy and obstruction counts.

“All of the defendants need to go home, even if temporarily, to provide their children with the guidance they were denied during those critical lost six years,” attorneys for the four men said.

Former NOPD Sgt. Arthur “Archie” Kaufman, who was charged and found guilty only in the alleged cover-up, has remained free on $100,000 bond since October 2013, shortly after Engelhardt threw out the convictions of all five men.

The four who remain jailed all were sentenced to decades in prison for opening fire amid the chaos in the days after Hurricane Katrina after rushing to the bridge over the Industrial Canal in response to a police radio report of an officer in trouble.

At their trial in 2011, numerous victims and officers painted a picture of a band of cops rolling up in a commandeered U-Haul truck and proceeding to fire an indiscriminate barrage of bullets at a group of innocent people. After the smoke cleared, the officers falsely attested that the people on the bridge were armed, according to testimony.

Several other officers pleaded guilty and testified for the prosecution about the firing spree that left 17-year-old James Brissette and 40-year-old Ronald Madison dead and four others injured.

Kaufman, then a homicide detective, was accused of managing a cover-up that allegedly included a failure to collect any evidence and the planting of a “clean” gun. The alleged whitewash also included invented testimony from made-up witnesses supporting the idea that Lance Madison, a civilian on the bridge, had fired on cops and then tossed his gun into the canal. Lance Madison was accused of trying to kill the officers.

Engelhardt initially sentenced Bowen and Gisevius to 40 years each in prison. Faulcon got 68 years, Villavaso 38 and Kaufman six.

More than a year later, Engelhardt seized on an online posting scandal involving top prosecutors in then-U.S. Attorney Jim Letten’s office. He ordered an investigation by special federal prosecutors into the extent of the online postings under stories about pending federal cases.

The scandal forced senior federal prosecutors Sal Perricone and Jan Mann, Letten’s second in command, out of office, and Letten retired under a darkening cloud.

Reports submitted to Engelhardt by the special prosecutors, John Horn and Charysse Alexander, have remained largely under wraps. But the probe revealed that yet another federal prosecutor, Karla Dobinski — who was directly involved in the Danziger case while based in Washington, D.C. — also had posted anonymously during the trial.

The judge issued his order rescinding the Danziger convictions in September 2013. Engelhardt found “grotesque prosecutorial misconduct” so horrendous he said he didn’t even need to find that the actions of federal prosecutors actually had tainted the jury.

“Retrying this case is a very small price to pay in order to protect the validity of the verdict in this case, the institutional integrity of this court and the criminal justice system as a whole,” he wrote.

A panel of the 5th U.S. Circuit Court of Appeals upheld Engelhardt’s order in a 2-1 ruling last August, dismissing the government’s argument that Engelhardt overstepped his authority in tossing out the convictions. The full appeals court last month declined to rehear the matter on a 7-7 vote.

According to a recent legal filing, Justice Department attorneys soon will decide whether to take the issue to the U.S. Supreme Court. In the meantime, the case is moving toward a retrial, although no new date has been set.

Meanwhile, Engelhardt apparently hasn’t given up on his quest to resolve unanswered questions related to the online commenting scandal.

He recently ordered Horn and Alexander to report by March 28 the “exact date” when each became aware that Dobinski had posted online comments about the Danziger case. Engelhardt also wants a list of those who reviewed the reports the two prosecutors submitted in early 2013.

Engelhardt is seeking the information ostensibly so he can rule on whether the lead trial attorney in the Danziger case, Assistant U.S. Attorney Bobbi Bernstein, should be disqualified from future proceedings.

The four jailed former cops, meanwhile, “have spent an extraordinary, nearly unique length of time awaiting a constitutionally fair trial because of the government’s misconduct,” their attorneys argued Tuesday in their motion for bail.

They did not propose a bail amount but suggested that GPS monitoring or other conditions “would assuage whatever concerns the court might have” about whether the officers would appear at a retrial.

Engelhardt previously denied bail to the four officers while his ruling was under appeal.

The four “have reason to be optimistic that they would not be convicted again,” their attorneys argued. “They believe they have found new evidence that will exculpate them and impeach the government’s witnesses.”

Follow John Simerman on Twitter, @johnsimerman.