The update takes the Finnish political milieu well into consideration, and seems reasonable on the face of it. The sudden massive growth of the SDP is, IMO, more than a bit iffy, after such a short time since the beginning of the economic crisis, though. As it is, the party ITTL doubles its vote in the 1930 elections, making it bigger in parliament than it has ever been IOTL. I understand that a worse depression than IOTL could boost SDP support, but it is unlikely it would tilt the elections this much to the SDP's favor. It was still just a bit over a decade from the civil war, after all. There was a lot of distrust towards the SDP among the supporters of the "bourgeois" parties, in the countryside especially, and I simply can't see so many habitual voters of the bourgeois parties suddenly turning to the Social Democrats.
When we look at the OTL elections in the 30s, and even after the war, the changes in party support changed pretty slowly. The fault lines between the right and the left were too strong for such a massive, sudden shift. The political protest being directed at just the Agrarians is also unlikely. The SDP were the biggest party in parliament, and had been in the cabinet just recently in 26-27 as well. The growth the SDP saw IOTL in 30 and 33 can be well seen in the context of the far left being broken like the far right demanded - its voters turned to the Social Democrats instead. Namely, this means the voters of the STPV that was banned due to the OTL Communist Laws: the SDP gain in seats in between 1929-33 is pretty much exactly the same as what the STPV lost in 1930. On the other hand, by 1933, the Agrarians only lost what they had gained in 1929. What the OTL saw, therefore, can be understood as the fault lines between the Agrarians and the left returning to "normal" in 1933, after a brief rise in Agrarian support, on one hand, and the reorganization of the left so that the far left was subsumed by the SDP due to the general campaign against the far left, on the other. This is to say that the effects the Great Depression caused in the Finnish political system IOTL were pretty small in terms of the fault lines between the left and the bourgeois parties.
In the conditions of deepening depression and agitation in both the left and the right, it is hard to see that the elections would lead to a Social Democratic government. Quite the contrary, Relander would probably appoint an Agrarian minority cabinet, or perhaps a Agrarian-National Coalition joint cabinet. If the Finnish government goes Social Democrat at this point, the moderates in the bourgeois parties would fear that this will galvanize the right against a "perversion of the results of the civil war" and only strengthen the Lapua movement and make it likely that the Civil Guards and the military might move right as well. Under such circumstances, the bourgeois parties would close ranks for the presidential elections. So, Tanner winning the presidency is unlikely. As it was, even the possibility of the moderate Ståhlberg winning was seen as a likely spark to ignite a Lapuan rebellion. Have anyone even a bit more left win would be worse.
So - if Tanner won, putting down a Lapua Movement rebellion would be much harder than IOTL. As president, Svinhufvud could moot the Mäntsälä rebellion because he was trusted by the conservatives and much of the Civil Guards and the military as "their man". He had the authority to cowe the right wing as a believable anti-Communist leader. With a Social Democrat-controlled government in the early thirties, there would a real possibility of more of the Civil Guards and soldiers joining a far right coup attempt, due to a belief that the Social Democrats in charge would not be trustworthy or legitimate enough and that the country was sliding towards a new leftist takeover and Communism. Whether or not the majority of the armed troops in Finland would follow the orders of the legitimate national leadership would be touch and go in such a situation. Even if Tanner could control the situation, I can see it getting much worse than with Mäntsälä IOTL, to the point of actual fighting and loss of lives. And that would be very bad for the future of the Finnish society, any which way we look at it.
In the worst case scenario, the combination of a Social Democrat government and a Lapuan insurrection in the early thirties could lead into a civil war, and/or a militant far-right takeover of the government.