WASHINGTON — Against a growing outcry over the surging price of EpiPens, a chorus of prominent voices has emerged with a smart-sounding solution: Add the EpiPen, the lifesaving allergy treatment, to a federal list of preventive medical services, a move that would eliminate the out-of-pocket costs of the product for millions of families — and mute the protests.

Dr. Leonard Fromer, a clinical professor of family medicine at the University of California Los Angeles just promoted the idea in the American Journal of Medicine. A handful of groups are preparing a formal request to the government. And Tonya Winders, who runs a patient advocacy nonprofit organization, reached out late last month to crucial lawmakers on Capitol Hill.

“We can save lives by ensuring access to these medications,’’ said Winders, chief executive of the Allergy and Asthma Network.

A point not mentioned by these advocates is that a big potential beneficiary of the campaign is Mylan, the pharmaceutical giant behind EpiPens.

An examination of the campaign by The New York Times, including a review of documents and interviews with more than a dozen people, shows that Mylan is well aware of that benefit and, in fact, has been helping orchestrate and pay for the effort.

The journal article says it was “drafted and revised’’ by a medical writing consulting firm paid by Mylan, in consultation with Fromer. And Fromer himself has served in the past year as a paid Mylan consultant — which he discloses as part of the journal article. The company has also contributed money to many other groups behind the effort, and it has met with them — and Winders’s organization in particular — to coordinate its strategy, the participants said.

The effort has accelerated in recent weeks, just as Mylan has faced a flood of criticism about its pricing of EpiPens. The retail price for the standard two-pack has jumped nearly fivefold since 2010, hitting $608 this year. Multiple lawmakers and regulators have opened investigations into the pricing of the product, which has virtually no market competition.

The idea being advanced is simple: If the EpiPen makes the federal preventive list, most Americans would have no insurance copay when getting the product. That means they could obtain the medication with no direct cost, regardless of its retail price. Mylan could keep the EpiPen at the current price, or perhaps raise it more, while keeping patient anger at a minimum.

Instead, the federal government, health insurers, and employers would pay the bill.

“In a way, it is brilliant,’’ said Rachel E. Sachs, a law professor who specializes in public health policy at Washington University in St. Louis. “We are all seeing them for what they are — the poster child for high drug prices right now, but they don’t want to be. And this tactic is nothing but a self-serving move, not a public-regarding one.’’

Mylan, in a statement, acknowledged financing “research, resource development, and travel’’ by the nonprofit coalition Winders formed in collaboration with the company to help push for the change. But, the company said, “we were clear in our corporate sponsorship agreements that the coalition would maintain control.’’

The company also pointed to steps it had taken to lower the price of the EpiPen. Mylan has announced more rebates for some patients and it is preparing to release a less expensive generic version.

The decision about whether to label EpiPens a preventive drug will fall to the US Preventive Services Task Force, a federally appointed group of physicians and public health experts.

The task force chairwoman, in a statement, appeared to all but rule out adding EpiPens to its list of recommendations. But a review of Mylan’s lobbying history makes clear that the company has an exceptional track record at influencing government policies, both in Washington and in state capitals.

Proponents of adding EpiPen to the federal list argue that it can prevent a fatal allergic reaction by stopping anaphylactic shock from progressing, if taken immediately.