In a way, they essentially became the Bull Moose Party, after leaving the Democrats. Maybe have them join the Republicans instead, or absorb the progressive and or northern wing of the democratic party as opposed to vise-versa.
They never really left the Democratic Party; they became absorbed into it when the Dems nominated William Jennings Bryan.
Honestly, I think the easiest way to do this is to have the Dems and the GOP to come under the sway of their conservative wings and nominate gold Presidential candidates. Although the Gold-Siver debate was not the key issue for the Populists, it was still a major differentiation between them and the major parties. With this, I could see them making further gains in the House and Senate in the 1896 election, although they will likely fall short of the Presidency.
The Populists were actually making major attempts to draw in Union and urban support during this period; both Eugene V. Debbs and, just as importantly, Victor Berger became involved with the Populists around this time (the later of which helped the make some major inroads into Milwaukee and Wisconsin). A strong showing at this point, as well as the continued dominance of the Conservatives in the two major parties, might draw further reformers into the People's Party. In such a situation, and assuming they choose a candidate with broad based support, they might have a real chance to win the Presidency in 1900 which would put them at the forefront of the Progressive Movement.
