I honestly believe Black Doom could still be the main antagonist of the game in this rewrite, although instead of making him and the Black Arms a bunch of random aliens, I came up with a crazy way of relating him to the Adventure saga (considering Shadow debuted in Sonic Adventure 2) and one of the most relevant elements of this franchise:
The Black Arms created/found the Chaos Emeralds, and brought them to Earth millennia ago.
I know, I know... it sounds nuts, to say the least, but read me out: how can a demonic-looking alien like Black Doom use Chaos abilities, skills that are linked to those who have made contact with Chaos Emeralds, elements that (apparently) only exist in planet Earth (or Mobius, or however we call Sonic's world)?
It's stated that Black Doom himself came to Earth over 2000 years ago, so seems likely that these alien guys can survive a veeeeery long time.
Now, why would these extraterrestial beings come to our planet? Heck, how did they even know there were rational beings living on the surface of the planet? Could they have visited Earth before?
Let's say they DID. And in that moment, they gave the Emeralds to, I dunno, let's say THE ECHIDNAS, likely the race whose history seems to be more linked to the Chaos Emeralds than no one else in this franchise.
Of course the Black Arms would keep someone protecting the Emeralds, perhaps an offspring genetically modified so it could adapt to the most hostile Earth's conditions, a creature that could also use the power of the Emeralds itself...
(Now, another crazy over-the top retcon here. Brace yourselves...)
...a creature like THIS:
"C'MON, DUDE, YOU CAN'T BE SERIOUS!" you might be thinking.
And yep, we're making a Shadow the Hedgehog rewrite so of course I'm not fully serious, BUT seriously, look at our boi Chaos and its alternate forms and tell me they don't look like freakin' aliens. Chaos Zero looks like an alien! And it even has three fingers, those yellowish eyes and sort of feels like the fusion between a Chao and a Black Arm.
So, to sum everything up, if I had to remake Shadow The Hedgehog and reshape its story, I'd keep Black Doom but clearly stating that he has roots deep into the Sonic lore. He wouldn't be just a random extraterrestrial warlord. If he happens to be Shadows biological father, Shadow's Chaos powers should come from somewhere that made sense, and what better way to explain Black Doom's Chaos powers than this one?
And I'm not even getting started on how an alien invasion could have been way more interesing if, instead of just falling from the sky, the Black Arms were already on Earth, waiting for the Ark to be (apparently) dissabled like it did at the end of Sonic Adventure 2...