NEW YORK — The first time I heard about “Girl From the North Country,” my thoughts pretty much coincided with those of Conor McPherson, the dramatist and director who would eventually bring it to exhilarating life.

“I initially thought, ‘Well, you know, it just felt like a bad thing to do,’ ” McPherson said by phone from Dublin recently. “Bob Dylan and a musical? Er, no.”

We would both end up being surprised — his change of mind, of course, being far more significant. For “Girl From the North Country,” closing Sunday after a highly successful 3½ -month run at the Public Theater, is in my estimation the best musical of 2018, on or off Broadway, and beyond. What happens to it next is still apparently up in the air, as it is not, despite a remarkable Dylan songbook spanning more than 40 years, one of those easy-to-transfer projects.

As a tale set in a Duluth, Minn., flophouse during the Depression, and stocked by McPherson with a gallery of hard-luck characters, the production doesn’t have the upbeat infrastructure of so many other, more commercial musicals. (The Public is a nonprofit organization.) I have heard it described by some as too much of a downer — as though the only emotional weather a mass American audience can endure is relentless sunshine.

It was with the musical’s value and the challenges to its longevity in mind that I wanted to write about it again, and have a chance to identify what has made it, for me, such a lasting high point of the year. We in the theater critic business spend so much time writing about plays and musicals at the outsets of their journeys that few opportunities seem to exist to go back and examine the impact of shows after a considerable portion of the public has taken a look.

And “Girl From the North Country” is one of those enterprises worth visiting again, as I did, in the advanced stages of its run in the Public’s Newman Theater. What I got from this second encounter with the American version of the show — which I had seen in its original incarnation in London — was a deeper appreciation of the profound effect that casting American actors in its 17 roles has had on the work. And of the achievement of one actor in particular, whose contribution has not only established her as a major musical theater talent, but also helps make the case for wider exposure of the musical in this country.

That person is movie, stage and television actress Mare Winningham, whose performance provides the emotional backbone of the musical. She plays Elizabeth, a mentally ill middle-aged mother who has never recovered from the death of a daughter. Amid the variety of hardships recounted by the denizens of the boardinghouse run by her husband (played by Stephen Bogardus), Elizabeth’s story is one of the evening’s most moving. Winningham’s rendition of the show’s best-known Dylan number, “Like a Rolling Stone,” becomes a kind of poignant anthem for all of the characters, each walled up in their own fortresses of pain.

Over the run, Winningham has tried to assess the spell Dylan casts over the Newman, and how McPherson managed to make a score of music from the 1960s to the 2000s speak for the realities of the 1930s.

“You see the audience — the songs belong to them,” the actress said from an office in the Public’s theater complex in the East Village.

“There was a moment in rehearsal when Conor talked about how each of the characters is on the precipice of survival,” she continued, explaining that the director sought to “strip us all of the sentiment that actors want to cling to.”

Whenever questions arose about illuminating the relationship between the songs and the story, McPherson told the cast not to worry. “Dylan will do it for us,” he told them.

“I felt that Dylan’s lyrics were so timeless,” McPherson said. “They’re almost romantic poems that come from any time. If you think of what was informing his development as a songwriter, it was those very well-crafted songs of the ’30s and ’40s that would have been coming through the radio. Ignited by the likes of Hank Williams, Woody Guthrie, but then also Buddy Holly, he was listening to music before rock-and-roll was invented, and then rock-and-roll crashed into it.”

You could sense in the original London iteration, born at the Old Vic Theatre and later moved to a commercial run in the West End, an accomplished cast that was exerting itself to play plain American folk from the upper Midwest. With the American and Canadian actors — among them such estimable hands as Marc Kudisch, Luba Mason, Sydney James Harcourt, Kimber Sprawl and Robert Joy — some of that artifice disappeared.

“What was interesting doing it with American actors was that it was a whole side of their energy that was available to them because they didn’t have to pretend to be American,” the Irish-born playwright said. “I kept saying to the cast, ‘Does this feel American?’ ”

It does, indeed, feel American, the world of “Girl From the North Country,” and evocative particularly of the perpetual sense of panic and emotional exhaustion that destitution can wreak. But what distinguishes this show from so many others that have used preexisting music by famous artists is that the repurposing not only undergirds the storytelling, but also changes the songs.

For Winningham, who has sung all her life and whose recording career has intermingled with her acting, the prospect of singing a Dylan classic was both exciting and daunting. “I was a little paranoid about ‘[Like a] Rolling Stone,’ ” she said. “It was the trickiest song, because it’s so iconic.”

It was her boyfriend who helped demystify the assignment, by explaining that the director had to sense her, not Dylan. “ ‘He’s going to want you to bring you to it,’ ” she recalls him saying. “ ‘You have to let go and bring yourself.’ ”

That notion of a personal spark invigorating beloved music is emblematic of “Girl From the North Country,” and may help explain why the desire to hear it again was stronger for me with this musical than any other of the past 12 months. The hope is that the closing performance on Sunday won’t be the last chance anyone else gets to hear it.

Girl From the North Country Through Sunday at the Public Theater, 425 Lafayette St., New York. 212-967-7555.