Disclaimer: I attempted to read the entire thread. I was confused. This is my own model.
Ships require 3 types of supply to function: Munitions, Fuel, and Consumables. Munitions includes things like missiles, fighters, bombs, assault landers, and ammunition for certain weapons. Fuel is pretty obvious, it's what makes the ship go. Consumables are things like water, oxygen, food, spare parts, and so on.
Military Supply Ships are designed by the player. These are designed just like normal ships, except their role is defined as "Supply Ship." (The role of Fleet Tender is similar, except it is treated as a normal ship for all purposes, its just a ship with a large supply hold) The tonnage of supplies carried is defined the same way it is for any other ship: excess hull space. Supply ships are built by shipyards, and therefore must be ordered. Supply ships, once built, are removed from the player's view, though their location is recorded.
Supply ships are assigned to groups of ships in a supply manager screen. Specifics are not included, merely: Assign X amount of Matriarch-Class Supply Ships to Battlegroup Z. These supply ships fill up with a generally equal amount of munitions, fuel, and consumables (modified by the needs of the fleet), and move to join the fleet. As much supplies as possible are transfered to the ships of the fleet. If the ship is now empty, it returns to the nearest friendly world to fill up and return.
If a fleet attacks when supply ships are actually with the fleet, they do not join in the attack, they are considered to have been left behind to join up later. If a fleet is attacked with supply ships present, they are on the battlefield. If a supply ship encounters raiders on its route, combat is initiated. This may or may not be player controlled at the player's discretion. However, this proposition assumes a total upper bound of combat time per turn, so dealing with all commerce raids would be time prohibitive. In the pre-combat screen (pick which engagements to participate in, give general orders to the ones you're not), the order to "Disengage and choose a safe route" is available.
If a ship is not fully supplied with munitions, it will be short ammunition. For example, a Wareagle-Class Missile Destroyer carries 6 2-ton missile launchers with a 12 missile magazine each. The missiles are all Deathknell V's, except each magazine has one Firestorm ADD missile. If it uses all 6 Firestorms to raze a planet, it would require 12 tons of Munition supplies. Note that even though different missiles are used, it still requires just a given tonnage. That 12 tons of munitions could have instead provided a Thunderbolt Strike Fighter to the fleet carrier, its all the same.
If a ship is not fully supplied with fuel, its in deep trouble. When running low on fuel, ships will limit evasive maneuvers in combat to attempt to conserve it. When ships run out, they are effectively useless until they can be resupplied.
If a ship runs low on consumables, a steady drop in combat performance ensues. If the ship actually runs out, it becomes a ghost ship.
Ships do not necessarily need supply ships to be resupplied. Fleets get filled up at friendly worlds. Sufficiently advanced races may be able to teleport in supplies, or at least fuel. Fuel can be taken from enemies that use the same fuel. Consumables can also be taken, though that is dependant on biological similarities. Munitions cannot be taken, even if you stole a Silicoid fighter you'd have no way to work it.
One more option is to conscript civilian frieghters for emergency resupply work (Paris taxis anyone?). These frieghters are generated based on technology a few generations old, and are never armed. This conscription will damage your economy, especially these frieghters are lost, and is a security risk with respect to espionage. However, it may allow you to save a starving/drifting/weaponless fleet.
Anyways, there's what I got. Fire at will