The PSNI has already come in for heavy criticism for protracted delays, running to six years, in disclosing documents on the nine contentious deaths in the early 1980s linked to the alleged security force policy.
The papers include files from the long-classified investigations into the killings by Greater Manchester Police Deputy Chief Constable John Stalker and Sir Colin Sampson, of West Yorkshire Police.
Northern Ireland's Senior Coroner John Leckey has been pressing the PSNI to make clear when the exhaustive disclosure process, which involves security checks, would finally be complete.
At a preliminary inquest hearing in Belfast, Dr Tony McGleenan QC, representing the police, said that the Chief Constable Matt Baggott was now in a position to give a completion date of the end of 2014.
"You have pressed us, you have pressed our client for an end point, and the end point I have been given is the end of 2014," he said.
Better to identify a realistic end point you can hold us to rather than an ambitious one which for other reasons may fall short.
Dr Tony McGleenan QC
Mr Leckey, who pointed out that it was now 25 years since the inquests were first ordered, expressed concern at the disclosure time-frame.
"Is it not possible to bring the end date forward?" he asked.
Lawyer for the coroner's office, Frank O'Donoghue QC, echoed Mr Leckey's reservations.
"It seems difficult to anticipate we are going to be in a position to commence this inquest even at the start of 2015, which we have been working to as a fall-back position and last resort," he said.
"I am concerned at a date being given as the end of 2014.
"I would be reluctant to walk away from today's PH (preliminary hearing) accepting the end of 2014."
To be perfectly frank there has been so much slippage in this case it may not even be the end of 2014.
Frank O'Donoghue QC
The barrister suggested that the chief constable be urged to "redouble" his efforts and divert more resources so as to bring forward the completion date to next Easter.
The case involves six people, including IRA men and a Catholic teenager, who were shot dead by the security forces around Lurgan and Armagh in 1982 amid claims there was a deliberate intention to kill them.
The coroner will also examine the deaths of three Royal Ulster Constabulary (RUC) officers who died in a bomb blast weeks earlier - an attack allegedly carried out by the IRA men, who were subsequently gunned down and therefore, seen as a potential motivation for the claimed shoot-to-kill policy.
Edited versions of the Stalker and Sampson reports were handed over to the coroner in 2010 after a long legal battle, but reams of top secret documents remain undisclosed.
Dr McGleenan said since the coroner had last raised issues about the length of time the process was taking, more resources had been diverted to the exercise.
He said that this had seen a further batch of files handed to the coroner's office.
"Since the last time we met there has been a movement forward in terms of deploying more resources in response to the exhortations made by your office," he told Mr Leckey.
Barrister Barry Macdonald QC, acting for the families of two of those killed by the security forces, said the progress was welcome, but expressed concern at the completion estimate.
"It would be churlish not to welcome progress that has been made but I do echo the sentiments of Mr O'Donoghue that it would be preferable to have a more advanced date," he said.
The police have repeatedly stressed the scale of the task they have been requested to complete and its associated strain on resources.
It involves reading and redacting a mountain of papers to remove information that could potentially threaten national security. Only individuals with appropriate security clearance are allowed to conduct the task.
Mr Leckey has also requested disclosure of classified documents related to the deaths from a variety of other government departments and agencies, including the Ministry of Defence, the Security Service, the Northern Ireland Office, the Home Office, the Foreign Office, the Cabinet Office and the Attorney General for England and Wales.
Dr McGleenan revealed that the PSNI chaired an inter-departmental meeting last week involving these bodies - apart from the Foreign Office - to discuss a "coordinated approach" to providing disclosure of the 57 different types of documents requested by the coroner.
The lawyer said he had not been given any time-frame on when this separate disclosure process would be completed and indicated that similar security assessments would have to be carried out on those files as well.
During the hearing in Laganside courts, Mr O'Donoghue also provided an update on the coroner's efforts to bring in extra resources to his office to work on the inquest.
His requests for an investigator and a ballistics expert to be hired have yet to be given the green light, with the Courts Service still considering the issue.
Mr Leckey expressed frustration that in the case of the ballistics expert, officials had informed his office that the decision would require an assessment by economists.
The coroner insisted that the discharge of his duties could not be dependent on the "view of economists".
"I have a very strong view on that," he added.
Another preliminary hearing is set to be scheduled before the end of the year.