Well this is way outside the thinking of the Nazis but what if they did what the Union did in the US Civil war on a larger scale and had dedicated track laying units that put down temporary track as fast as they could to get their logistics as close to the front as they could, then carried it from there with trucks. They would have to find a way increase production early so they had enough production to ship to the front
They would also have to concentrate on building Locomotives, rolling stock and trucks/half-tracks so they would have some way to make use of the above increased production.
They would also have to have additional engineering resources improving the rail behind so that it didn't collapse during the spring/fall mud.
The way I see it there are several problems with these ideas -
1) Where does Germany get the additional materials to increase production enough to both build enough rail to make a difference and build enough Locomotives/rolling stock and trucks/half-tracks to move it to the front.
2) Where does Germany get the engineering resources to build thousands or tens of thousands of kilometers of new rail fast enough to make a dent in the logistics needs of a modern army. If they can do it they have a chance to do better, I am just not sure they can do it.
3) What about partisans? Is this just setting up a fixed route that is easy for Soviet partisans to attack? Frankly rail is easier to knock out than road, but it carries 10-25x as much for lower fuel costs so is it worth the additional troops needed to protect it?
4) Is the Soviet Union just too big for this to work? It worked in the US during the Civil war but the distances were shorter.
5) Is this too out there for the Nazis to even think of?
Tom.
Edit: Thought of one more possible problem...
The Nazi did have dedicated teams of railway workers, who were under civilian command. The basic process need is to unpin the rails, move them into the narrow gauge distance and re pin to the wooden railroad ties. After that, the crew needs to repair any damage done to the railroad by the war. It is more a labor issue than a material issue on fixing the tracks. The Germans did not make the workers work on weekends and holidays at the start of the war, so it is easy to speed up the process with an order from Hitler.
At the corp level and below, the level of fuel, ammo, and food decline constantly through the first few months of the war. Besides the lack of narrow gauge rail, what was the bottle neck. Was it lack of supplies, lack of trains, or lack of transport from the unloading rail head to the soldier? I am not sure about which is the main bottleneck.
But on the original POD for the post, if Germany goes to full wartime production and has more supplies, more trains, and more replacement equipment, they could certainly done better than OTL, but it probably does not win them the war.