How about a game like Truxton, where you have to go through five times to see the last of the ending.
For the Genesis/MegaDrive version, the endings can be viewed consecutively without even playing the game, by using a Game Genie.
1. Insert Truxton + Game Genie into the console.
2. Make sure the Game Genie power switch is on, then power on the console.
3. Use Game Genie code SANA-BJZY, then press Start to display the Truxton title screen.
5. Press Start to begin the game, and after the opening music plays, the ending will play. (Note, if start is not pressed then when the demo sequence starts the ending will also begin to play.)
6. Don't touch anything else and the endings will keep playing until Game Over occurs.
As an additional point of interest--the first loop of Truxton on the Genesis/MegaDrive version actually uses simplified patterns when compared to the arcade's first loop. Therefore, loop 2 is actually closer to the arcade version's Loop 1 difficulty. Here's how to go directly to loop 2 at the very start of the game.
1. Perform steps 1 through 5 as listed above.
2. When the ending starts to play, switch the power switch on the Game Genie to OFF.
3. When the ending finishes, the game will start at the next loop.
However, to remain on topic with the 1-All/1-CC discussion, I would probably refer to 1CCing each loop and count a 1-All if all levels (or loops) were finished in a game that ends (or ends after multiple loops). For example:
* I 1CC'd the first two loops of Flying Shark/Sky Shark. (The game never ends, so I can't really claim a 1-All.)
* I 1-All'd U.N. Squadron, arcade version, likely set to an easier difficulty in the arcade that had that machine. I could also just as easily state I 1CC'd it, but I tend to think that 1-All de-facto indicates that the game ends rather than loops forever.