There is an existing bug with the Aircraft carrier unit ability that makes one of the best solutions not work well in the current game.
The bug is that when you have aircraft loaded onto an aircraft carrier of any kind and then that aircraft carrier moves into a port (or other land square), when you send the aircraft on any missions like bombing or recon, then they will automatically unload from the aircraft carrier after the mission is completed.
The solution to extending bomber range technically needs this bug to be fixed to work seemlessly.
The solution to the bomber range limit is to create a land unit called the "KC135" and give it movement of 6, 8, 10 or even 100. Then set the transport capacity to 2, 3, or 4 and enable the transport aircraft ability. Give the KC135 the all terrain as roads ability and triple its range. The Tanker basically carriers the bombers out to half its movement range and refuels them in flight so they can then bomb targets 8 tiles away. When the automatic carrier unload bug is fixed, then the KC135 can return to its airport after refueling the bombers for the flight home as well.
Note that all this discussion is a little bit ridiculous from a game play standpoint because the AI players cannot possible understand or use this combination of unit abilities since they are not programmed to recognize the threat or apply the strategy.