To stop the bloody war between the two Five Points gangs, gangleader Paul Kelly must defeat his rival Monk Eastman in a boxing match, with the winner’s gang taking the disputed territory.

Give us the era then the main conflict.

In 1800 (whenever) the heads of the two gangs running New York agree to a winner takes all boxing match to end a bloody war.

The exception of using historical character names in a logline is valid for when the names hold currency - Jesus Christ, Al Capone, Barak Obama.

In your case, the characters have been obscured in the pages of history, and while real historical figures, their names mean very little if anything to most readers.

It would serve you best to describe their function and role instead.

.... Maybe:

"After a corrupt Tammany Hall politician demands that his Election Day head-busters stop their own bloody turf war for the welfare of the community, the Godfather of the Mafia agrees to fight a rival gangleader (as logical not in the same gang) in a boxing match;? the winner taking complete control of Five Points, New York. "

Hmmm, this makes it look too much like "Gangs of New York 1"

I guess the writer of the book/makers of the movie "Gangs of New York"? took the 20th century 'Tammany Hall Hall Election Day head-busters' facts and put them in the? middle of the 19th century.

Not sure if there still is a story left. Research can be a B*tch.