I can understand a desire for vengeance and international guarantees, but it would seem more likely that most Finnish governments would go for reasonable expansion and reparations in the form of currency, industrial products rather than aim for doubling the land area of their shaky, slowly recuperating nation. But if Kola and Karelia are in fact handed forcefully to the Finnish government (by the victorious allies) and the Finns have little say in the matter, I can understand those borders. Hopefully they come with a fair-sized package of economic incentives to boot.
Your point is sound. However, be mindful that, according to the TL, the Euro allies must do a serious committment to integrated economy and collective defense in the late phase of WWII already (the EEDA's foundation is scarcely one year after the end of the war), so Finland comes to the peace conference with a reasonable expectation that the Allies shall subsidize its economic redressment and defend its security in the future. And the Allied mood is to give the Russians a peace settlement that is manageable concerning Russia's size, ethnic-cultural borders, and future livelihood but really punitive enough to prevent it from recovering top-tier great power status too easily. Without resorting to large-scale ethnic cleansing or leaving massive Russian minorities in Eastern European countries, this means pushing Russia back to Muscowy borders, and this is what the Allies implement. The Eastern Karelian border fits quite nicely in this scheme.
We may expect that the Kola-Karelia annexation is the result of a combination with the Allies prodding Finland to get it for strategic reasons, and the revenge-minded Finns not being so averse to the annexation because of Allied guarantees abour economic incentives and collective security. Actually, this peace treaty is a win-win outcome for Finland, they get the Euro Plan Marshall money, the extra land, and the immediate European integration (this balances the scales somewhat for the brutality of Soviet occupation).
When I say overextended, I mean in the context of Finnish resources, both actual and perceived. ITTL Finland never had the experience of easily driving back the Russian armies like in fall '41 IOTL. Rather to the contrary, they even lack the experience of the mythical defensive victory that was the OTL Winter War. TTL Finns do not seem like a people to base their defensive strategy on holding huge land areas against potential Russian armies. Thus, prudence and caution in expansion would be an understandable frame of mind for the new Finnish leaders.
Yup, but again, they have the (correct) expectation that they can rely on European anti-Russian collective defense in the future, which liberated the country once already. And ITTL the EEDA is more than enough of a worthy match for shrunken Russia, even on a conventional level alone, not to matter nuclear supremacy going to last a long while. Remember, this Europe is going to have an "American" attitude to military power.
But I see you aim for Finland to become, in terms of the national frame of mind, a "OTL post-1991 Estonia" analogue ITTL. It is possible, if Finland really gets definite international guarantees and there are promises of, say, strong troops from allied nations stationed in Finland after the occupation in Russia ends.
This is what I wholly expect to happen, indeed. Think it this way: after the Anglo-French-Germans (and after a while, all the recovering "minor" allies in Scandinavia, Central and Eastern Europe, and ex-Soviet space) make wholehearted committment to collective anti-Russian defense as soon as WWII winds down, it entirely makes strategic common sense for them to project their defense as forward as reasonable, within the frontline states (Finland, Baltics, Belarus, Ukraine). This ensures that a Russian comeback is denied "Near Abroad" assets as much as possible and the war is kept as far as possible from the European core.
ITTL we ought to expect at the very least the European equivalent in Finland and the ex-Soviet states of the NATO troops in West Germany and quite probably much more than that. Even if the EEDA shall have to split its defense potential between the Russian and SL borders, and to spare an amount to defend the colonies and repress nationalist insurgencies, we are talking of at least 300 million population even in the early post-WWII period, with a First World economy, cutting edge technology and American-level militarization. They are going to enjoy conventional supremacy in an Euro-Russian rematch to a degree that NATO could only ever dream of. And of course, they are going to keep nuclear supremacy for a long while, so if Russia really misbehaves again, the EEDA may just decide that twice is enough and glass the steppes.
Even ITTL, Finland was initially sacrificed to the Soviet Union: you need a lot to overcome the typical Finnish pessimist idea that foreign powers west and south are ready to forsake Finland as a minor inconvenience in terms of the bigger picture.
See above. And ITTL the Euro-Americans pulled the land equivalent of the Normandy landing for Central and Eastern Europe, fighting Stalin till total victory. I think this ought to dispel previous Finnish feelings of betrayal about being initially left alone, to a very great lot. The allies made several initial mistakes, the anti-Soviet coalition took a while to assemble, but no one is perfect, the final result matters, and Finland was liberated. Besides, in the EEDA defensive strategy, abandoning Scandinavia to the Russians would be sheer foolishness.