Bring me the head of Samuel Gompers.
Gompers was the king of American trade unionism for decades and focused solely on craft unionism and conservatism. Bump him off and give European style trade unions a dominance to allow a broad working-class movement to form.
Just look at Britain for comparison. The Socialist Part of Great Britain was an intellectual talking shop interested in Marxism. The Labour Party was an alliance of trade unionists dedicated to lifting up the working class. The word 'socialist' did not appear in Labour's 'official' writings until 1918, oddly enough when the intellectual Fabians began to greatly influence the party's structure.
I was once heard Tony Benn at a talk. Someone asked him 'how do we return the Labour Party to socialism?'. He replied 'Labour has never been a socialist party, simply a party with socialists in it'. Waggish but it does sum up the make-up of British, Australian and New Zealand Labour movements.
Though it wont help on its own, maybe getting rid of Debs himself? His blood and thunder style made him a celebrity but this ensured many people thought he was a revolutionary in the making. Look to the Populists, the Progressives and Farmer-Labour movements for a Kier Hardie figure to lead but not dominate 'American Labour'. A broader base not relying on a totemic figure might allow for better staying power and the ability to creep up the ladder of power in the United States, gaining local and state power to enable a more realistic run at the Presidency in time.