On the other side of the debate, Ardoyne priest Father Gary Donegan claimed the "moderate voice" of nationalism in the area was prepared to compromise.
The site occupied by loyalist protesters on Twaddell Avenue has remained longer than most observers predicted. The numbers manning it have steadily dwindled over the years, but some remain.
The cost of the three-year policing operation required to monitor the camp is approaching £20m.
It was established in 2013 after the Parades Commission prevented Orangemen passing the nationalist Ardoyne along a contentious stretch of the Crumlin Road as they returned from their traditional Twelfth of July commemorations.
Similar restrictions have been put on parades in the years since, with rioting in the area in 2015, but the primary objective of the camp is allowing the three Orange lodges stopped in 2013 to complete their homeward journey.
Mr Beattie said if that happened, the camp would go and the focus could be shifted to finding a more permanent resolution to the annual dispute.
Commenting ahead of a major parade yesterday to mark the 1,000-day landmark, the senior Orangeman added: "The resolution to our mind has always been simple and it still remains simple - toleration of the six-minute parade up the road completes the journey and takes away the problem and takes away the protest.
"If the lodges were allowed to return home, the dynamic changes and the obstacle is removed. The playing field levels and therefore more constructive conversations could be had.
"If the parade is allowed home, I stand ready, as soon as that parade is up the road, to go into any form of conversation that is necessary to seek a long-term solution to the problem.
"I always like to look to a positive and I always try to think there will be a resolution sooner rather than later."
"We would hope the parade would be allowed up the road long before July 2016."
Contacts between protagonists on both sides of the disagreement continue in the background.
The chances of resolution are complicated by the presence of two residents' groups in the Ardoyne, one of them with a more hardline stance than the other.
Fr Donegan said he felt the position "most representative" of people in the area was focused on finding a solution.
He said any agreement could not be a "stopgap or plaster over an open wound".
"Let's actually make this once and for all a situation where, okay, it isn't perfect for everybody, everybody is going to have to take a hit on this, everybody is going to have to swallow hard but, at the end of the day, it's for the future of our society and the future of the children of both of those communities," he said.
The priest at Holy Cross church also insisted that any accommodation had to be struck at a local level.
"You get all sorts of well-meaning people come up with hare-brained ideas as to how to solve these things, but they haven't lived a single night here," he added.
The cleric said the nationalist community had come to almost ignore the sight of the camp as it had no real impact on their everyday lives.
But he said he regretted the cost of policing it. "When you are based in an area of real social deprivation, then you realise what £20m, what £10m could have done in both communities," the priest added.
"(You see) what you could do for kids in the area if you had spent that kind of money on them and developing the area."