That leaves the Norway garrison, the Balkans, and the Baltic. The POD presented is relying more on Ukrainian and Vlasov forces for the Eastern front. Even without doing this, pulling out of the entire Baltic states once the siege of Leningrad is lifted could be a doable way to shorten the line and release a couple of corps ,and the command staff from one of the two armies in Army Group North as well as the command staff of Army Group North itself. Hitler stated he wanted to keep the Baltics/ Kurland to maintain German naval superiority in the Baltic and use it for u-boat training grounds, so our alternative government would have to give that up. It would also release more Soviet forces, but they would have less space to attack. Finland would throw in the towel earlier, but that just means the Norwegian garrison has to stay in place.
The OTL Soviet operation against Finland was a sizable one. The so-called Vyborg–Petrozavodsk Offensive involved altogether 35 divisions, 4 fortified regions, 4 tank brigades and 17 tank and assault gun regiments. They were supported by over 220 artillery and rocket launcher batteries, and around 1500 airplanes. All in all, maybe over 450 000 men were involved in different ways.
IOTL, the Finns lost Eastern Karelia but managed to stop the Soviet attack on the Karelian Isthmus. By late July, the Soviets wrapped up the operation, not having reached their goal of breaking the Finnish army and knocking Finland out of the war. Practically, they had started to withdraw best units involved in the fighting, to send them to the German front, since the first week of July after the attack bogging down in what the Finns call the Battle of Tali-Ihantala.
Now, if the Germans have withdrawn from the northern Baltic area, especially Estonia, before the crucial stages of this attack, the Soviets gain significant strategic advantages which would have probably turned the battles on the Isthmus and on the Bay of Viipuri to the Soviets' advantage. The Finns fall back in disarray towards Helsinki, and make desperate attempts to create new defensive lines between Viipuri and the Finnish capital. This, in turn, leads in political and diplomatic terms to one of two things - either Finland, as you said, throws in the towel, or it decides, for some time, to continue the fight, even if it seems hopeless.
Why would the Finns continue to fight? The answer is that prior to the battles of the summer of 1944, Moscow's proposal for Finland included punitively heavy terms and practically amounted to an unconditional surrender. IOTL, after the success of the defensive battles, and reaching Germany early being a bigger priority, led to Stalin finally in the fall offering Finland a conditional armistice with comparatively lighter terms. The Finns could not accept surrender in early 1944 because they still thought that their strategic position was good, and they could get a better deal. In August 1944, after losing a lot of land and men, they realized that the conditional deal Moscow now offered was the best deal they could get.
Here, the maths are different. If the Soviets are successful in beating the Finnish army on the Isthmus, they will not give up demanding surrender with heavy terms. And this would in many people's opinion mean that Finland should keep fighting rather than lay down and die. There is, of course the possibility that the Finnish leadership sees the writing on the wall and accepts that surrendering is the logical thing to do, under the circumstances, What ever we can say about the Finnish wartime leadership, fanatics they were not.
The point I would like to make here stems from what I have written above. Whether or not the Finns give up in between June and late August 1944, more Soviet success against Finland would in any case lead to the Red Army needing more-than-OTL troops in the Finnish front for longer - either to beat the Finnish army and finally take Helsinki and the rest of southern Finland, or then kick off the early stages of the occupation of Finland. Or, as it might be, both. When in IOTL the USSR could withdraw the great majority of the troops it had used for the Vyborg-Petrozavodsk Offensive and shift them south against the Germans, here a significant part of those men, at a guess from 200 000 to 400 000, would need to stay in Finland and surroundings for months longer than IOTL.
Apart from beating, pacifying and occupying Finland, there would also be the case of the German troops in Finnish Lapland. If there is no conditional deal like IOTL, where the Soviets could use the Finnish military as its catspaw to evict the Germans towards Norway, here the Red Army will need to do this itself, or at least it will need to send enough troops north to contain the German 20th Mountain Army in where it is, awaiting an upcoming operation to attack through Finnish Lapland to Finnmark.
What this all means is that, comparatively speaking, the Soviets have less troops to send against the Germans here than IOTL, in the months following TTL's counterpart to the Vyborg-Petrozavodsk Offensive against Finland. While in the great scheme of things 200 000 to 400 000 troops may seem like a drop in the bucket, I'd argue that the absense of these troops would to some extent at least slow down the Soviet advance, especially as the Germans have shortened the lines early, and avoided things like the formation of the Courland pocket.