As to what the Reichsbahn might have done given the opportunity, is pure speculation. They need time to collect intelligence (which we know from the accounts of the FED that they lacked.) If so they may have identified the fact that the Soviets had not upgraded the Polish eastern network. This means a second Otto Plan to upgrade this 350 km gap between the upgraded Polish network and then the Soviet network. The plan can be made smaller because you do not need the surge capacity required for the pre-Barbarossa build up so instead of 7 railway lines, perhaps 5 lines of lower capacity (especially as HG Nord can be supplied by sea to a large extent) and instead of 3 months and 300,000 tonnes of steel a smaller amount and shorter time. But ideally you need to use all the assets of the Reichsbahn to achieve it.
Once you are onto the Soviet network, there is another choice, changing the gauge on two main lines per Heeresgruppe area is the easy bit, you then need to build capacity by adding signalling, sidings, shunting yards, engine depots of the correct size, working engines (there are sufficient engines across Europe but the Reichsbahn does not control them - so you have the choice of building more or moving the ones you do have) and rolling stock. Or you can retrain all your railway men to new operating safety standards and run the railway with less capable signalling in the Soviet manner, using lower speeds and bigger trains run to a different standard (or run by the local railwaymen who by and large stayed put). But retraining tens of thousands of men on new operating procedures is a large, complex task. (The German military's solution of using captured rolling stock was never going to achieve any real capacity - there is no example of a country leaving behind large amounts of undamaged engines when invaded not since 1917 in the Ukraine. Poland 1939, France 1940 all evacuated their rolling stock with time to spare. Any hope of that had to wait until you had won the war, not during it.) But it does allow you to gain a considerable capacity from lines that lack a lot of equipment but only if you provide sufficient engines to make it work. The Germans need locomotive columns as well to provide lots of motive power. Running trains in the Soviet manner is not enough if there are not enough engines, depots and men to run them, you need everything in place. As a guide we know that the Soviet mobilisation plan envisaged 360 odd trains a day running to the border, so the track is there for the Germans to run 200 odd trains a day for the invasion. Remember that they planned for 75 trains a day.
But if the GTR is utilised properly for connecting the Supply Districts to the troops over 300 km, then you have to put in place two main lines per Heeresgruppe to deliver 60+ trains a day from the border to the Supply District. HG Mitte actually has 3 main lines in its area and a couple of secondary ones, so upgrading one main line is possible even if you have to use the other ones in the meantime. Big effort on these main lines for a distance of 600 km over July and August is a large task but possible.
The conclusion drawn is that to achieve long distance operations, you have to put a serious effort into achieving it utilising national resources, just as the US and British Empire did at sea and the USSR did on land. The optimum for Germany was to use her huge coal reserves and railways to achieve this rather than as many have proposed to use scarce petrol and motor vehicles. It is still a large task and there are a number of different ways of achieving it but all of them are expensive in different ways. The simple fact is that this concept was a very long way from German military thinking which was to run a short term, shoestring logistical operation, win the battle quickly and then sort out the rest after the campaign is won. In that sense Fall Barbarossa represented a campaign beyond the capacity of the military system to deliver, 3 months and 600 km was the Germans limit both in terms of transport but also in other areas such as replacement men and weapons, ammunition, etc. A serious railway effort using all the nations resources surely would have got them another 600 km and another 3 months but were the other items going to be there?