The battles facing oysterman Kevin Lunny and his family business advanced in state bureaucracies and in federal court last week, as lawyers submitted their final briefs to push an appellate court to prevent the cannery from being shut down. On Monday Mr. Lunny’s lawyers argued to federal judges that the federal government overstepped its authority by attempting to convert to wilderness an estuary in which the state of California has reserved fishing rights.

Drakes Bay Oyster Company has been pushing the Department of Fish and Wildlife to take a more assertive stance in defense of the oyster farm, and commissioners who oversee the department discussed their legal options in closed session at a meeting in Santa Rosa last week that drew both supporters and opponents.

Meanwhile wilderness advocates unleashed new allegations, immediately denied by Mr. Lunny, that the cannery understated the costs of unwinding its operations in documents submitted to the state.

Environmental groups also pushed back against the argument by Drakes Bay advocates, including celebrity chef Alice Waters, that the public interest would be undermined if courts allowed the National Park Service to evict Drakes Bay.

The oyster farm is gearing up for a protracted lawsuit challenging a decision by former Secretary of the Interior Ken Salazar to not issue a new permit that would allow continued harvesting. But before the lawsuit goes forward the oyster farm must convince an appellate court to prevent an eviction that could destroy the decades-old business. Oral arguments for the injunction order will take place on May 14 in San Francisco.

Drakes Bay on Monday filed a brief that accuses the federal government of pursuing an “obsession” to shutter the oyster farm and attempts to pry open the alleged flaws in their opponents’ legal arguments while rehearsing several arguments of their own. Congress intended to speed the issuance of a new permit for Drakes Bay in 2009—not exempt the denial of such a permit from judicial review, as the government successfully argued to a lower court judge—the brief states. Drakes Bay lawyers say Mr. Salazar’s decision violated a number of laws, including requirements that major federal actions be underpinned by sound science. Drakes Bay lawyers also stressed that Drakes Estero is falsely being converted to a legal wilderness status, contending that fishing rights reserved by the state of California and an ongoing state lease for Drakes Bay’s offshore operations preclude such a status.

In a statement this week, Neal Desai of the National Parks Conservation Association said Drakes Bay had estimated just $10,000 in costs for cleaning up the estuary in statements to officials for seven years, despite more recently filing court documents saying those costs could top $600,000. “Taxpayers should be outraged that they may have to foot the bill for cleaning up the significant mess that could be left behind by this unsustainable oyster operation,” he said.

Mr. Lunny disputed the charge, saying that the escrow account required by his lease was set before he purchased the farm and is managed by state officials, an assessment that state officials endorsed.

Mr. Desai and the Environmental Action Committee of West Marin also dismissed a brief by Alice Waters and others who wrote that the loss of the oyster company would have deleterious impacts on the Bay Area’s restaurant business, food and environmental quality and the livelihood of the aquaculture industry’s workers. They cited noise disturbance of harbor seals and birds, the presence of an invasive tunicate and the coastal-commission order as evidence that the oyster farm is “far from being environmentally benign,” causing harms that weigh more heavily than the social impacts of closing the business.