Nice game, and a good AAR. The few random mud turns can be a pain, but so they are for the Russian side as well. I would say the random weather does benefit the Axis defense in mid war quite a bit by requiring the Soviet to keep a low pace/penetration depth when attacking, else risk having your spear heads cut off-- which are usually the best units you have. It is just that the 41 rush is so tight that you can only allow little to go wrong as Axis, but who know how history would have looked if they had had a much more rainy summer than they did. Perhaps the war wouldn't even have lasted until D-Day then. Fate... or dice rolls.
The key to LG -- decisive use of AGN's Panzer force in that sector right from the beginning, and not getting PG IV side-tracked towards Kalinin or anywhere else. It may seem boring to push the AG via Pskov directly to LG, but I think this is the best way to go. Sending a Panzer Corps West past the landbridge north of Peipius can be sound when the direct resistance in the area towards Novgorod and the Volkov is stiff, but else I think bullying your way in there seems to work in most cases, and the earlier AARs. The terrain there isn't exactly best Panzer terrain, but Wehrmacht is qualitatively so superior that even if the Soviet player sends all initial reinforcements up there and allows AGC and AGS to roam free, you still have the better chance to force your way to LG's back door. And the alternatives, like going through the poor terrain via Staraya Russia and Demyansk through the Valdai hills and coming up on the East side of the Volkhov/Novgorod means a narrow attack channel through much worse terrain, the best defensive terrain on the map in fact, and a very long supply line -- that has little prospect a seems like handing your cards to the Soviet side.