I'm looking for research looking at the influence of fiction on changing elite/public behaviors and opinions

(Apologies for the short answer; I'll expand it if I find more extensive resources.)

My go-to keyword for this would be storytelling in science communication, through which I found the following:

• Using narratives and storytelling to communicate science with nonexpert audiences (2014)
• Storytelling: the soul of science communication (2019)
• The Role of Narrative in Communicating Science (2009)

For more decision-maker-oriented literature:

• Storytelling and evidence-based policy: lessons from the grey literature (2017)
• (Blog) Storytelling for Policy Change: promise and problems (2016)

From a cursory reading, this is focused on short fictional stories that concisely illustrate a point, as a way to drive insight more easily. Something very targeted.

I'll have to dig more into the effects of longer works of fiction; I don't have quick references about this at the moment.

Some examples (I'm considering fiction generally and not just written fiction):

• The film The Day After was seen by 100 million Americans and was instrumental in changing Reagan’s nuclear policy.
• «President Ronald Reagan watched the film several days before its screening, on November 5, 1983. He wrote in his diary that the film was "very effective and left me greatly depressed," and that it changed his mind on the prevailing policy on a "nuclear war". The film was also screened for the Joint Chiefs of Staff. A government advisor who attended the screening, a friend of Meyer's, told him "If you wanted to draw blood, you did it. Those guys sat there like they were turned to stone." Four years later, the Intermediate-Range Nuclear Forces Treaty was signed and in Reagan's memoirs he drew a direct line from the film to the signing.» (Wikipedia)
• «Director Meyer and writer Hume produced The Day After to support nuclear disarmament with the ‘grandiose notion that this movie would unseat Ronald Reagan’, and the nuclear freeze groups heavily exploited the ABC movie as a propaganda.» (Hänni, A chance for a propaganda coup?)
• Arthur Koestler’s Darkness at Noon deeply influenced Edward Teller, whose views about the Soviet Union were central in his efforts to persuade the US to develop the hydrogen bomb.
• The short documentary film If you love this planet influenced Canadian PM Pierre Trudeau.
• The mini-series Holocaust motivated the abolition of the statute of limitations for war crimes in Germany:
• «In 1978 the major breakthrough into general consciousness of US citizens came with the showing on prime-time television of a four-part series simply entitled Holocaust, which was watched by nearly 100 million Americans. The fictional drama that followed the lives of a Jewish family, exposed to the full horrors of the Holocaust, and an SS man who rose to a leading position in the implementation of the extermination programme, captured the imagination in ways that scholarly literature could never do. Jewish organizations maximized the subsequent publicity opportunities presented by the success of the series to spread awareness of the Holocaust still further, both in Jewish and non-Jewish communities.
  In West Germany a year later the showing of the series was a sensation. Holocaust was watched by around 20 million viewers (around half of the West German viewing population), who were transfixed by the personalized and highly emotional dramatic depiction of persecution and extermination. People empathized with the victims and recognized the monumentality of the crime as they had never done before. ‘A nation is shocked’ was the verdict of one scholarly analysis of the impact of the film.“ ‘Holocaust has shaken up post-Hitler Germany in a way that German intellectuals have been unable to do,’ commented the widely read weekly Der Spiegel. More than three decades after the end of the war an American film, criticized by some as reducing the destruction of the Jews to the level of a ‘soap opera’, had opened up the sense of national guilt. The following year the Federal Parliament (the Bundestag) abolished the statute of limitations on war crimes, permitting further legal prosecution of perpetrators of the Holocaust. The film was widely seen as playing a significant role in the decision.» (Ian Kershaw, The Global Age, ch. 8)
• Nikolai Chernyshevsky's What is to be done had a more profound influence on Lenin than even Marx's Kapital, and is plausibly a causal antecedent to the Russian Revolution.