It’s a hard time to be a Founding Father if your name isn’t Alexander Hamilton.

The runaway Broadway success of “Hamilton: An American Musical” has meant that Thomas Jefferson isn’t even the sole attraction in his own home-turned-museum, Monticello. Visitors can take a standard house tour—or a $40 “Hamilton Takeover” one that focuses on Jefferson’s political adversary.

Long after its 2015 Broadway debut, “Hamilton” continues to make the Revolutionary period hip, and to the dismay of many history buffs, steal the limelight from other Founding Fathers. Fans of the other giants of early American history have been trying to fight the tide and grab some attention for their overlooked favorites. It hasn’t been easy.

On a recent afternoon, Monticello tour guide Carrie Soubra stopped in the library of Jefferson’s sunlit private suite to try to shore up the former president’s reputation, taking a dig at Hamilton along the way. Yes, the musical portrays Jefferson as a self-absorbed patrician, she said, but he trusted the voice of the people more than his rival did.

“Alexander Hamilton declared we should have a president for life,” Ms. Soubra said, pointing to an engraved copy of the Declaration of Independence, of which Jefferson was the principal author. “That sounds a lot like what this was trying to get rid of.”

In Philadelphia, crowds line up for a Hamilton exhibit at the National Constitution Center, but a beer-trolley tour led by a Benjamin Franklin impersonator is no longer offered because of lack of interest.

Warren Royal, the owner of Royal Bobbles in suburban Atlanta, says he produced a run of nonpresidential Founding Father bobbleheads a few years before the musical. He made Hamiltons, Franklins, Thomas Paines, John Hancocks and Sam Adamses.

After the musical hit Broadway, sales of the Hamiltons skyrocketed, outselling all other founders but George Washington. Hamilton is now closing in on Negan, a zombie-apocalypse survivor on AMC’s “The Walking Dead.”

Mr. Royal discontinued Paine and Hancock. Other founders are foundering, including the nation’s fourth president, James Madison. “He’s no Elvis, I’ll put it that way,” Mr. Royal says.

Historian Nancy Isenberg, author of “Fallen Founder: The Life of Aaron Burr” and other books on Revolutionary leaders, published a series of essays saying Burr was principled and progressive, not the “stand-for-nothing” sycophant portrayed in the musical. She says she was inundated with emails from “rabid fans with an attachment to an imaginary, invented Hamilton.”

“That’s not history,” she says. “That’s rooting for your favorite team.”

Sarah Maria Everett, a 30-year-old James Madison superfan and impersonator living in Juneau, Alaska, says she is “appalled and confused” by the hit musical’s depiction of Madison as unstable. She says the biggest problem for her favorite president is public ignorance.

Yet she has scant opportunity to don her tricorn hat and plead his case, with a lone coming appearance this summer in a July Fourth parade. No theater groups have agreed to perform her five-hour play, “Jemmy Madison: The Mind and the Man Behind Religious Liberty.” Jemmy was Mr. Madison’s nickname.

“There is not a lot of demand for James Madison in Alaska,” says Ms. Everett, who is considering impersonating German composer Richard Wagner in the future.

One Philadelphia-area Franklin impersonator, Brian Patrick Mulligan, posted a tongue-in-cheek audition video when casting directors were recruiting for a “Hamilton” national tour. His headshot was the $100 bill. The show’s casting director didn’t reach out, and Franklin remains absent from the show.
“It’s so young and hip and fresh,” Mr. Mulligan, 58 years old, says of the musical. “I can understand why they wouldn’t have an old man in the show.”

Mr. Mulligan has a few gigs lined up as Franklin, including an AARP internet commercial. He supplements his income with appearances as his backup characters, which include Winston Churchill and Uncle Fester from the 1960s sitcom “The Addams Family.”

Descendants and supporters of Burr, who killed Hamilton in an 1804 duel in Weehawken, N.J., have debated how hard to push back on the play’s characterization that Burr dishonorably fired on Hamilton.

“The play adopts the theory as true that Hamilton deliberately missed Burr,” says Stuart Fisk Johnson, a criminal-defense attorney distantly related to Burr who heads the Aaron Burr Association. “Throwing away your shot, they called it. But no one really knows what happened.”

The association debated sending a letter of protest to playwright Lin-Manuel Miranda. Its members couldn’t agree on whether to take a stand.

A spokesman for Mr. Miranda didn’t respond to requests for comment.

“Some members really leaned on me to make a big stink,” Mr. Johnson says. “We thought it’s going to make the Aaron Burr Association look like a bunch of kooks.”

Some of the group’s 80 or so members complained when the association took no action, and one, the group’s webmaster, quit in protest, a blow since no one else knows how to update the website, Mr. Johnson says.

The group did decide to protest statues of Burr and Hamilton erected in Weehawken, recently sending a sternly worded letter to township Mayor Richard Turner.

“The statues are despicable,” explained Antonio Burr, an association member who has impersonated his forebear at debates and a duel re-enactment. “Burr looking at Hamilton with intense hatred, and Hamilton is shooting in the air and looking like he is receiving the Good Lord.”

Mayor Turner didn’t reply to the letter, according to the association. The mayor didn’t respond to a request for comment.

“What are we going to do about it?” Mr. Johnson says. “We can’t issue a duel anymore.”

Veteran Jefferson interpreter Bill Barker recently joined the staff at Monticello as curators experiment with programming to reverse a recent dip in attendance.

He made his debut at a “Pursuit of Happiness Hour” on the west lawn earlier this month. Mr. Barker prepared a raft of responses to questions about Hamilton, ready to respond to questioning teens while posing for selfies.

But he says it is possible that Jefferson ends up a bad guy to a generation of fans.

“They would have every right if they should choose,” he said, speaking in character. “That is a founding principle of our nation.”

For now, boosters of non-Hamilton founders are pinning their hopes on the planned 2021 revival of the Tony Award-winning musical “1776.” It stars Franklin, Jefferson and Adams. There is no Hamilton.