My concept of ZOCs may be used for this:
http://forums.civfanatics.com/showpost.php?p=8441568&postcount=6
Enemy communications could be cut off by fast attacking units, spies, bombers etc.
On the other hand, defenders can destroy (or not to build) roads close to their borders (maybe one road that passes through the hill fort with plenty of fortified machinegunners in it) slowing enemy advance. There also can be a mission introduced for ground units, preventing from enemy units destroying improvements (just like the ships one).
I really, really like this idea. It has a lot of potential. Granted, it needs some tweaking in parts, like how to display supply lines and culture in the same tile, but still, great work.
Now, I think what supply lines actually do should be discussed. By looking at your diagrams, even though it's meant only to show the effects of supply lines, perhaps culture and military occupation should be combined and displayed as occupied territory (again, pulling from CivRev here).
Any tile occupied by a unit and all tiles which can be reached and returned from in a single turn will override any culture in those tiles, unless you are at peace with the civ that owns those tiles. The more soldiers you have on a tile, the more "cultural influence" they give off. The greater the enemy's culture, the less of a defensive bonus the units will receive while fortified.
As long as you have cultural influence in a tile, even due to military occupation, you will be able to improve the tile. Now of course, in almost all cases of this, you'll want to send workers to build forts deep in enemy territory, for easier conquest.
Now, even if there are no enemy units to counteract your military influence, if the enemy's cultural influence is too great, the territory will be disputed instead of under your control (due to resistance of locals). Military units within a disputed tile due to overwhelming culture will suffer damage each turn (from constant attack, soldiers going AWOL, and what have you).
Not having a culture connection (supply line) to your empire will not affect your soldiers, but the supply cost will increase for each tile of enemy culture the suppliers have to go through. It is preferable to keep a supply line in place to minimize spending.
Finally, units can perform hit-and-run attacks on any city/fort within range, provided they are already stationed in a unit/fort. Same rules as above apply. Also, hit-and-run attacks can only be performed as long as the path does not go through enemy territory (disputed territory is fine.)
So, one particular strategy you can employ is to set up a supply line by occupying territory, build a fort within two tiles of an enemy city, station your attack force in it, and start sapping their defenses with combined melee and siege. As long as you keep the supply line open, you'll be able to quickly swap out your wounded soldiers for fresh ones, maintaining a merciless onslaught until the city is too weak to defend against a real attack.
If I can also work out a way to allow new soldiers to arrive on the scene AND attack in the same turn, this will no doubt speed up wars greatly. But if I were to do that, then I'd have to say Simultaneous Turn Resolution needs to be put in the game, so that both quick victories and quick defeats will be equally possible.