An idea to consider would be logistics units.

1. Each map would have at least one hex marked as main Supply Base. If you lose control of these your armies will lose supply (until you grab it back). Protecting your own and trying to overrunning enemy ones these would a key in each battle.
2. Units without supply will constantly lose some small fraction of fuel, ammo and initiative even when not engaging in combat or movement.
3. New class of Supply or logistics units: These can be Truck, Half Track, Fully Tracked, Horse Cart, Alpine mule or even panje wagon with different terrain movement characteristics like regular units. (Perhaps Cargo aircraft for encircled pockets?).
4. Supply units have a zone of influence (based on their movement points and terrain) and can supply ALL land units as well as airfields and ports in their zone of influence.
5. Supply line: Supply units can continue to supply as long as they are near a Supply Base Hex or within the zone of influence of another Supply Unit.
6. If a supply units loses contact with main base(s) it can continue to normally supply the units in its zone of influence for a few turns – Mules, Panje wagons for one turn, half track or full track supply tractors for two turns and normal trucks for perhaps three turns reflecting their load capacities.This gives a little resilience to the supply system so that a random interdiction by a aircraft doesn’t immediately kill the while supply chain.
7. If a supply unit is damaged beyond a point (say half points) it can forward only half the supply. So if a unit tries to resupply it gets only half rations. This allows partisans, air interdiction to slow down enemy advance.
8. Normal units have the regular resupply mechanic – they must stop all action for one turn to rearm, refuel or add replacements.

I think I am making this sound very complicated but in my head it is a fairly simple system.