Going back through Shadow the Hedgehog's endings, this particular Black Arms Shadow seems to be from the Mostly Dark Ending variant, wherein Black Doom's plan goes off without a hitch, and Shadow becomes his right hand. As this is not the worst case scenario (Pure Dark, everything will die or be conquered), that means this Shadow did, at minimum, 2 missions following Black Doom's orders, or followed him obediently up until the ARK and chose not to destroy the ARK's defenses. I'm not about to suggest he could have done any of the heroic routes then backtracked onto the dark routes because of the implications of what he did to the settlements.
This is crucial imo because that means this Shadow had his final showdown in the Black Comet, which is only accessible through either killing the president, reliving the ARK massacre in which he kills every G.U.N. soldier, or going through Iron Jungle and destroying all the G.U.N. robots there. I'm willing to bet this Shadow still has a shred of sentimentality for the ARK and what it meant to him.
This is a Shadow who loathes humanity, but not the world itself, was told he was created to be Black Doom's weapon, and accepted it as fact. To get him to change his worldview again would be a monumental task. But not an impossible one.
/blathering
Anyways, DC to infiltrate the Restoration is lowered. Send in Belle maybe? She makes friends, Eggman gets intel. It's win-win!