The billionaire claims Mr McGowan's attacks on him were serious enough to harm his reputation even amongst people who already viewed him negatively.
In an outline of closing submissions published by the Federal Court on Monday, Mr Palmer's lawyers said an award of aggravated damages - which would allow for a payout above the cap of $432,500 - was entirely appropriate.
Mr McGowan, who is counter-suing Mr Palmer, has made his own appeal for aggravated damages over public comments made by the Queensland businessman.
The premier is claiming qualified privilege as a defence for labelling Mr Palmer an "enemy of the state", among other insults.
It requires proof there was a legal, social or moral duty for him to say those things.
Mr Palmer is defending various comments he made on the basis of qualified privilege, and substantial and contextual truth.
The mining magnate had sought up to $30 billion in damages over a 2012 decision by the former Liberal state government not to assess his proposed Balmoral South iron ore project.
The McGowan government rushed through extraordinary legislation in August 2020 to prevent Mr Palmer from suing the state.
Mr Palmer's lawyers referred in their submission to messages sent by Mr McGowan to media mogul Kerry Stokes, the chairman of Seven West Media.
After being tipped off by Mr McGowan to the introduction of the bill, Mr Stokes' daily newspaper The West Australian ran front pages variously depicting Mr Palmer as the movie villain Dr Evil, a cane toad and a cockroach.
In one message, Mr McGowan said "mealy-mouthed tut-tutting by some people" about Mr Palmer's rights made him sick.
"This is the language, and the attitude and state of mind, of someone consumed by malice," Mr Palmer's lawyers said.
Mr McGowan had sought to "blacken (Mr Palmer's) name at every opportunity", they said, describing the attacks as relentless, personal and vicious.
They also argued the premier was untruthful in his evidence, accusing him of misrepresenting advice from the state's chief health officer.
Mr McGowan's lawyers said their client had given honest testimony and expressions such as "enemy of the state" were clearly intended figuratively.
In his evidence, Mr Palmer said he was scared because provisions in the legislation protected the government from criminal prosecution.
Referring to the fictional character James Bond and his "licence to kill", Mr Palmer told the court: "I didn't know what the limits might be."
Any suggestion Mr Palmer had a genuine fear for his physical safety was "inherently incredible", Mr McGowan's lawyers said.
There was also little evidence his reputation had been injured, they added.
Justice Michael Lee last week flagged each man could receive a nominal damages sum, describing them as political combatants with entrenched reputations.
He will reserve his judgment after receiving final written submissions later in April.
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