I know I've been beating that horse carcass for quite some time by now, but I still hold out hope for this and do see it as a genuinely possible outcome.
The OTL Russian Civil War, in the grand scheme of things (i.e. ignoring foreign interventionists, the anarchists, and the Greens) can roughly be drawn up as a war of three cliques - the Tsarists, Republicans, and Communists - split between two factions (the Whites and Soviets). Within the Soviets you had relative unity between the varying cliques of socialists, in spite of their comprising a spectrum between vaguely democratic elements and what would later become Stalin's clique. Contrasting this, the Whites had vast ideological diversity within their main compositional guilds, what with the Tsarists divided between multiple claimants and multiple ideas about how strong the monarch's role in government should be, and the Republicans between social democrats, liberals, and conservatives. The latter were defeated and politically silenced, leaving a very limited subset of vogue ideological vehicles for the state to operate in; this, coupled with the prevalence of communist hardliners among the remaining political elite, lent itself to the effective centralization of totalitarian power under the Marxist-Leninists.
TTL's Russian Civil War has a similar overall structure (three cliques divided between two factions), but compositionally the makeup consistency between the status quo faction (the Tsarists) and the revolutionaries (the Republicans + Marxists) has been nearly flipped. The Tsarists are, while divided between constitutionalists and absolutists, reasonably united in support of a single government apparatus - there aren't any Kirill loyalists anymore, and Mikhailovich isn't really contesting the throne against his son. Contrast the anti-Tsarists, who have people ranging from Kerensky to Antonov to Zinoviev to Lenin in positions of political relevance; such heterodoxy does not lend itself to an easy and stable peace, but it also makes any one faction gaining substantial enough support to take on and suppress the others hard. This incentivizes working with other groups in coalition to advance positions of mutual interest - something that the key actors of the Republic have been doing throughout a lot of the story, from the base alliance between Kerensky and Zinoviev to more popular forms of solidarity as seen in the people of Petrograd after its conquest - which is a basal element of parliamentarianism and one further weakening the notion of revolt due to the value in appealing to others rather than warring on them.
It's by no means guaranteed in the event the Republic wins the Civil War (in the event the republic pisses the soviets off too much, it's possible the various left-wing factions could unite against the government given similarities to the Lvov government of Xenia I's empire), but I certainly feel it's possible for political necessity and mutual weakness to establish seeds of cross-party dialogue in the near-term postwar period, and from then on internal conflict fading as a motivator due to the positive feedback loop of normalized inter-party negotiations. But we'll just have to see how the story goes, and wherever Russia ends up is liable to be reached only after a long and painful journey to at least some degree.