This is an idea that is well beyond my meager abilities to write...
The concept, in a nut shell, is that the 100 years of war is not nearly so... clear cut. When Aang wakes up, the world isn't the Fire Nation vs. Everyone Else... it's an "Each Element for Itself" free for all across the entire planet, and even that can be misleading...
Long version: Sozin's comet wasn't nearly as powerful as in the original story (or at least its effects were much shorter lived) and the other nations at the time were equally ambitious...
First, the moment the comets effects start to wane, the Earth Kingdom and the Northern Water Tribe launch separate assaults against the fire nation, in an attempt to wipe THEM out. This fails, but it starts a world of war that will last for a century, with the people of each element trying to eliminate and/or dominate all others.
This is made even more complicated in that the Fire Nation failed to wipe out all the Air Nomads. Those that remain stop being Monks and Nuns, and organize much more like the historical Mongols... including city-destroying raids.
It gets even more complicated as one considers that most of these nations have factions within themselves, vying for control... the most obvious of which be the division of the Northern and Southern Water Tribes.
This is the world Aang wakes up to.
Now, to make things easier, the canon characters should still be around, but they will all be different, too.
For example, in this world, it was the Norther Water Tribe that chose to consolidate all the Water Benders under their own flag, and those of the Southern Tribe that wouldn't go willingly were taken by force. Katara is still the last Southern Water Tribe water bender, but she doesn't want to go to the Northern Tribe to learn... she wants to try and rescue any of her fellow Tribesmen that are being held by the Northern Tribe.
I haven't really come up with more beyond that, save for some vague idea of the White Lotus Society trying, and failing for a century, to stop the wars... but as I said, this is well beyond my ability...