But projects to cut the northern Lend Lease route would run into the same problems that projects to assault the city ran into ITTL, that there are too many things going on elsewhere. Its also hard to get a POD going without German units being drawn or not sent somewhere else. As awful as the siege was, there were good reasons why the Germans just didn't take the city.
It's what? 700 km East to cut the Arkhangelsk-Moscow line at Vologda starting from Volkhov through swamps and forests while hindered by a single track rail? Not sure how they do that by any stretch of the imagination. The USSR is big and empty, there's not much of value between Leningrad and Moscow.
Greater freedom for shipping supplies through the Baltic would take some pressure off the overstressed rail network too.
Not really, the Soviet rail networks splayed out from Moscow on purpose to make it more difficult for invaders. The Smolensk-Rzhev Salient is still reliant on Moscow-Minsk line, unless the Nazis want to drive all the way from Riga/Leningrad to Moscow past another 1000 km of Soviet defenses.
Source:
https://tile.loc.gov/image-services...001:g7001p:ct004328/full/pct:25/0/default.jpg
I think the main value of taking (or at least threatening to take them such that the Soviets destroy them) the oil fields for the Germans is in denying the Soviets sufficient fuel to wage the continuous offensives that allowed them to bludgeon the Wehrmacht without respite. The difficulty of actually extracting and processing oil once they're back up and running would be a daunting task for the Germans, even if it's not outright an impossible one.
They simply didn't have the rail capacity to supply troops needed to hold an extended southern front like OTL (See map above, there's no major railways that run East-West in Southern Russia), let alone ship crude 3000 km back to Germany where it's needed to refineries they didn't have. The most "likely" proposal IOTL, given that Romanian riverine shipping capacity was already overstrained trying to transport its domestic supply to Germany and thus not a factor was the utilize the only remaining capacity within the Axis: Italy via the Black Seas straits with total dominance of the Mediterranean.
IOTL the TMB (technological petroleum brigade) estimated that the task of drilling out boreholes and repairing filled up shafts, given the expertise, pipeline, transport, and equipment needed were all in shortage or not produced by Germany in any significant quantity. The earliest estimate assuming Baku taken in 1942 (somehow...) was a year for Maikop, two for Grozny, and they never even bothered to plan for Baku. How they would get tankers or pipelines back to Germany past partisans and aircraft raids was dismissed by bravado.
A good deal of the TMB, given their engineering skills and experience are in dire demand everywhere. While I don't think they'll reassign them given the promise of oil the overall German engineering effort will suffer in the meantime.
Finns would be hard-pressed to refuse future German demands to attack Sorokka. Cutting the northern line of Murmansk Railway here is not impossible, but holding it against Soviet counterattacks would be a harder feat.
Murmansk itself will hold regardless, since defending wilderness with only a single road going through it is easy enough.
Further down the line the fall of Leningrad would make it much harder for Finland to leave the war the way it did in OTL.
For starters, the bulk of the Finnish Army and field fortification efforts would be focused on Eastern Karelia, creating a completely different operational scenario for potential Soviet future counteroffensives.
Leningrad frees up 2 Finnish corps. it doesn't change the fact that the Murmansk railroad is hundreds of kilometers away from Finnish railroads-how are the Finns going to supply a drive across the frozen wilderness against a USSR that can ship in troops and supplies by the trainload? The only railroad at the time in Northern Finland ran along the Baltic, the closest railroad to the Murmansk line was Joensuu to Sortavala, still 200 kilometers within from the Soviet border.
this is my reasoning for a larger naval effort in the Baltic, they have nowhere else to rob. they could weaken the defense of Leningrad if they stopped the Soviet evacuations to the city. (there was the similar scenario with evacuations, by sea, from Odessa to Crimea)
the German KM could bring up some of the WWI-era ships and/or captured coastal ships to try and shell Leningrad? allow the siege guns to be moved south.
Nope, 400 km of minefields in the Gulf of Finland.