The federal government has given Drakes Bay Oyster Company until July 31 to shut down the cannery and oyster shack and remove its personal property from the shores and waters and Drakes Estero, according to farm owner Kevin Lunny.

That property includes the cannery equipment, 20,000 oyster bags containing millions of oysters and five miles of oyster racks—though the farm and the National Park Service disagree on who is responsible for the latter, which has a longer 90-day window for removal.

Over a week after the Supreme Court declined to hear Drakes Bay’s case against the Interior Department, thereby denying the farm an emergency injunction to remain open while fighting its lawsuit, Mr. Lunny and his lawyers are still deciding whether or not to pursue the case. On Monday, the parties’ lawyers met in federal court in Oakland; both sides said settlement discussions were progressing, though government lawyers noted that if an agreement on the terms of the wind-down was not reached in the next month, the park could take “administrative action.” Department of Justice attorney Stephen MacFarlane said the government had informed the farm that it no longer had authorization to operate.

Mr. Lunny argues that the racks, which do not float but instead are affixed to the estuary’s floor, are “structures” and therefore the property of the park. The farm’s special use permit lists their personal property, but does not list the racks, he said.

The removal of those racks—12 feet wide and 10 feet tall, comprising over a quarter of a million feet of lumber—will be no easy task. “That’s a huge construction project,” Mr. Lunny said. “You’d have to be a magician to do that in 90 days.”

And although the farm has been planting fewer oyster seeds, there are still millions of oysters in the estero. According to Mr. Lunny, the government is considering offering him more time to harvest so that fewer oysters are wasted, but he is unsure whether that harvest will be feasible given the government’s other demands.

“Their vision is that we land them on the beach and truck them [out]. But we have F.D.A. rules, state health rules. With no refrigeration or water… they’re making suggestions that may not be plausible,” he said. Even if the farm were to be given six months more to harvest, it could perhaps reap just half of what is still growing, he added.

This month’s shutdown will leave all but half a dozen of the farm’s 25 employees out of a job come July 31. Legal Aid of Marin will be giving the workers legal advice at a meeting on Thursday, said Paul Cohen, a lawyer for the nonprofit. “Our staff is our primary concern. These are people that have really dedicated themselves, some for decades,” Mr. Lunny said.

Spokesperson John Dell’Osso wrote in an email, “[W]e are reinitiating contacts with the workers about relocation benefits that those who live on site may qualify for, and will be working directly with those families. As we work through this process, all employees who currently [live] on-site at DBOC may remain. Not all workers live on-site, however, and we are also working closely with West Marin Community Services to engage caseworker services to support all of the employees.” Point Reyes National Seashore officials did not answer a list of questions about what the workers were entitled to, directing most inquiries to the Justice Department.