OTOH I honestly don't know if Finland was that strategically important for the Soviets for them to go to such lenghts. Giving a good beatdown and taking land concessions - certainly. But completely overturning Finnish applecart - debatable.
It seems pretty clear that the original Soviet goal was a quick, victorious war in which the Finnish forces are trounced and a puppet government is installed. While no "smoking gun" documents with Stalin ordering it with those exact words has surfaced (and probably never will), I think at least the amount of circumstantial evidence to support that conclusion is exhaustive.
The Red Army orders were to occupy Finland and Stalin seems to have fully expected it to be a cakewalk. And after the Red Army takes Helsinki, there would really be no reason for it to leave - in that case letting Finland off with a mere slap on the wrist would have been out of character for Stalin, and in fact for the USSR too. And let us not forget that during the war the USSR did broadcast to the world that it will not accept the Finnish government as legal but has made a peace with a new Finnish government, the aforementioned puppet regime under Kuusinen.
Stalin was playing for keeps. Unfortunately for him, the Finns resisted too successfully, the war dragged on without a decisive victory, and it started to look like the war will escalate with an Anglo-French intervention. This all ruined the Soviet plans, and before a suddenly bad situation turned to catastrophic, Stalin proved his political acumen by ditching the Kuusinen regime, making a quick peace with bourgeois Finns and squeezing off some concessions to save what face he could. This was a lot less than he would have wanted, originally, but it was a lot better than the worst possible scenario for that trainwreck of a war - the thing Stalin feared the worst, encirclement by the Western Allies and a Germany that has suddenly made a peace with them to attack their common enemy, the Union of Soviet Socialist Republics.