Constable Carroll was the first member of the PSNI to be murdered. He was ambushed and shot dead as he responded to a 999 call at Lismore Manor, Craigavon in March 2009.
A court heard on Thursday that police had subverted and manipulated appeal proceedings brought by two men jailed for murdering the police officer.
Senior counsel for one of the pair seeking to overturn their convictions claimed detectives' bias had undermined confidence in the prosecutions.
As senior judges reserved their decision on the joint challenge by Brendan McConville and John Paul Wootton, they were urged to find an abuse of process had occurred.
McConville's barrister also argued that the case against him has been "destroyed" by new evidence branding a key prosecution witness a compulsive liar.
McConville, 42, of Glenholme Avenue, Craigavon, is serving at least a 25 year sentence for the murder. Wootton, 22, formerly of Collingdale, Lurgan, received a minimum 14-year term.
The case against them at the non-jury trial involved DNA and other evidence.
Prosecutors contended that Wootton's car was near the scene of the attack and driven off within minutes of the killing.
However, his legal team insist absolutely no evidence exists to link him to any role in the shooting.
Gun residue was found on a coat linked to McConville which was later recovered from the vehicle.
Central to the prosecution case was the evidence of a man identified only as Witness M who claimed to have seen McConville in the area around the time of the killing.
But this man's father has now testified to the Court of Appeal that his son is a liar and Walter Mitty-type character who couldn't have been there.
As the eight-day hearing drew to a close, police came under further attack for arresting Witness M's father after he supplied an affidavit accusing his son of dishonesty.
He was detained following a covert surveillance operation at his home on suspicion of withholding information before being released without charge.
The detective who headed the hunt for Constable Carroll's killers testified that he believed this man may have been held and threatened at gunpoint before making his statement.
But Barry Macdonald QC, for McConville, contended: "His evidence tends to establish the abuse of process of which we complain.
"Specifically his arrest, detention and interrogation represented a subversion of the appeal process."
Dismissing the belief that the man had been abducted by gunmen, Mr Macdonald claimed police refused to consider the possibility that he supplied his affidavit voluntarily.
"This gives rise to issues about the rule of law and the respective roles of police and the courts," he said.
"Witnesses should be cross-examined in court by counsel under judicial supervision in accordance with the laws of evidence.
"It's not open to police to pre-empt appeals, no matter how important the case may be, by arresting a witness and then subjecting him to interrogation in police custody under threat that he's liable to be charged with a serious criminal offence if he doesn't withdraw his affidavit."
With the defence unable to interfere with prosecution witnesses, he argued that the same rules should apply for both sides.
The three judges hearing the appeal, Lord Chief Justice Sir Declan Morgan, Lord Justice Higgins and Lord Justice Coghlin, were told: "Their (police) conduct clearly had a chilling effect both on (Witness M's father) and on anyone else who might dare to come forward to give evidence which would not support the prosecution case."
According to Mr Macdonald, the father's testimony "effectively destroys the evidence on which this entire prosecution hinged, the evidence of Witness M."
He said no attempt had been made to challenge core claims by the new witness that his son was "a dishonest fantasist who believed his own lies and was in many ways a pathetic character to be pitied rather than blamed".
Scathing criticism was also directed at the police for their alleged failure to investigate the possibility that a note found in McConville's remand cell in 2009 - with the car registration details of the Maghaberry Prison governor - had been planted by jail staff.
When former prisoner ombudsman Pauline McCabe reached that probable conclusion, the senior investigating officer blamed her for "clouding the waters" on the chances of successfully prosecuting McConville for the discovery, Mr Macdonald told the court.
He claimed it may also reflect the detective's attitude on the evidence in the murder inquiry.
"All of that indicates, we say, a lack of fairness and impartiality on the part of this investigation, the murder of Constable Stephen Carroll, to such an extent that confidence in the integrity of this prosecution process is undermined," Mr Macdonald insisted.
Urging the judges to quash the conviction, he concluded: "The net effect was that the police did manipulate this appeal in more ways than one."
But Ciaran Murphy QC, for the prosecution, contended that the new evidence from Witness M's father was "inherently unreliable".
The barrister pointed to his difficulty in remembering events on the night of the murder, claiming he appeared to be piecing together other bits of information.
According to Mr Murphy, Witness M's father had been under pressure and accepted being untruthful himself on one aspect of his account.
Incidents of a bus being set on fire outside his house and a man allegedly pointing an imaginary gun at him in a bar were highlighted.
Mr Murphy said: "He's under a clear impression that the community are looking after him and that he's an asset to the community.
"It's noted in the audios he said he would the hero and all would revolve around him and that there were people watching him from the Continuity IRA.
"He's therefore under pressure to perform."
He told the court that despite the "clearly personalised" allegations against the senior detective, police acted as they felt they should, based on their information.
Following closing submissions Sir Declan said all material put before the court had to be considered before a verdict is reached.
He confirmed: "We will reserve our judgment but we will give it as soon as we can."