So, basically, assume the Socialist Revolutionary Party of Russia manages to beat the Bolsheviks at their own game of radicalizing the masses and forming a coherent new state out of that by 1919.
Why play the Bolshevik game? Isn't it a much better idea for the SRs to base themselves on the soviets to push through immediate Constituent Assembly elections and the creation of an institutionally solid republican framework? Judging (not only) from their results at the CA elections in December 1917, the SRs had nothing to fear; they could have easily won a strong democratic mandate.
Some semblance of party pluralism is maintained, but the SR's manage to carry out their political agenda.
Why only "some semblance"? The SRs did not need to rig the elections or marginalise their opponents, they had broad popular support and could have carried out their political agenda through democratic (and once there's a constitution also constitutional) means.
What the SRs needed to do was not to radicalise the masses, they needed to convince their own leadership to stop buying the liberals' bullshit about the situation being unfit for elections in Russia, to stop buying the Mensheviks' bullshit about Russia not being at the stage of a socialist revolution yet and in need of a bourgeois democratic period first, and to go ahead building a new republic based on the support and will of the people who actually did support them and their political program.
What would be their proposals for tackling the ethnic minority question?
Unclear. The SR program envisioned a federal design for a future democratic Russia, but you never know if a leadership recruited from among their ranks would manage this properly or bungle it so badly that the centrifugal forces of OTL are still in motion.
What would their relationship with the Ukrainian movement be?
In Ukraine, the Ukrainian SRs were strong, too. The problem here is the course of the war - if Ukraine doesn't fall under German occupation, things look a lot better than if it does.
What about land reform, collectivization
Land reform was their no. 1 point on the agenda. They must deliver on this. Chernov brought in more than ten drafts for it, but Kerensky's government never did anything with them. If the SRs don't go ahead with this, they lose their rural support.
But no collectivization in the sense of OTL. Traditionally, Narodnik parties supported the idea of the obshchina, and the SR had militated against Stolypin's reforms aimed at dismantling them. But the SRs' views on the matter changed slowly in the 1910s. It is important to remember that the SRs were really the party of the peasantry, so whatever course an SR government would take, it would aim (well, aiming is not hitting, but still) at improving the peasantry's lot. In my "Feeble Constituion" TL (see my signature), this goes so far as to mean, when push comes to shove, to favour rural interests over those of the industrial proletariat e.g. in the question of food price caps.
The SRs were deeply committed to this. (And for good reason, too.)
amnesty to dissidents from the civil war
What civil war? The SRs are faring best if there is none. If it starts, the SRs are in danger of not being to mobilise their men as fast as their opponents.
Would TTL's Russian politics still be prone to strongman influence
That depends, I think you can plausibly envision a system which is at least as prone to corruption as Mexico's PRI system, but there's no strict necessity for it. A rather uneducated electorate is probably receptive to lots of things, but that doesn't mean it going to come like that.
Secondly, would SR Russia attempt to export the revolution like the Bolsheviks briefly did?
That depends on the course of the Great War and on the interaction with the other great powers. As a tendency, I would think the drive is a lot weaker.
What about military buildup?
Again, could go lots of ways. Primarily the financial situation of the SR-controlled Russian Republic.
Would they still attempt to retake the Baltics and other lost provinces of the empire?
Maybe they are not lost at all... If they're lost, their chances are as slim as the Bolsheviks'.
Could they be open to an early integration of Russia into the League of Nations?
Probably also depends on the course of the Great War. If SR Russia stays in the war and on the Entente side, it may be one of its founding members. If it goes the Brest-Litwosk way (over which it could stumble and disintegrate...), it's difficult, not necessarily from Russia's point of view, but from that of the others.