Actually placing new units in Berlin and then railing them might be worse than just placing them near the front as the the strategic move costs lots of supplies (but no fuel).
The HQ missing supply is just a glitch in the network, but from now on the occasional unit will be OOS, after crossing the Dniepr line the rear most units will be more and more OOS as the supplies go to the units furthest advanced into the enemy territory.
You can not build enough infra to cover all provinces!!! I had to realize that a long time ago :/ there are certain paths that will gradually emerge as you advance and sometimes they will not be used after you advance beyond a certain point. Identifying the paths is the key they will mostly be single province paths and might change suddenly when you liberate a province that is far behind the front line which then becomes the best path.
When you are nearing the Stalingrad line and your starting to get problems with front line supplies, withdraw all armour and many planes, then all mech, then the rest of the bombers. This might be less of a problem here as you have few axis troops to help you, but will eventually be the case if the fight continues.