This is a pretty major oversimplification of Napoleon's relations with Russia.
The Russians were not "bought off with Finland". They didn't particularly want the place: their foreign policy had been southward-orientated since the Great Northern War ended and they ended up taking it over because Sweden happened to have its capacity to resist utterly broken and the Swedes had been persistently irredentist for the last century (that had actually mostly wound up after 1792, in government circles at least, but the Russians have never been willing to give anyone the benefit of the doubt when it comes to protecting Petersburg).
The Treaty of Tilsit happened because once Russia accepted that there was nothing to be done about French control of western Europe, and the French accepted that they could not (in 1807) invade Russia, they had no immeidately conflicts of interest seperate from the general wariness of an upstart, expansionist power.
Finishing the war with Sweden (and thus having more resources available to finish that with the Ottomans) was one thing that made the Russians drift away from the Tilsit settlement, but there were more important factors. The commercial strangulation of CoSys made literate opinion increasingly hostile to the French alliance, and then the 1809 war demonstrated that, tactically speaking, everyone was on the level now, and at the same time brought the problem of Poland back to the fore.
It was the resultant alienaton that made the Russians resolve to break with CoSys (which happened before 1812). We didn't "convince" them, they convinced themselves in accordance with their own interests (we were actualy pretty crap at convincing people: our diplomacy in Austria could sink to "We have money! We'll give you money if you throw Metternich out of the window!"

.
Now, obviously, a big power on the edge of Europe and a big power in the centre will find it hard to agree on everything (especially the Near East) in the long term; but if Napoleon's plans in Spain don't go arse-end up, which delays or averts 1809* and creates problems for Britain, we might make a compromise peace before Napoleon decides to resolve the Russian question shortly and sharply.