Because I couldn't sleep. This idea wouldn't let me rest. But my writing skills are not such that I could do this idea justice, not to mention an inherently low energy drive. So, without further ado,
After the body swap, it isn't AziraCrow that return to Earth. It's another Demon and Angel. AziraCrow are imprisoned in heaven and hell respectively. They are in the pits of each. Forgotten or more likely ignored and left to rot or lose themselves.
The demon and angel sent back in their respective corporations know that they had switched and will need to switch back. That they will be living in the corporation of the other for an indeterminate time.
They must attempt to capture the traitor by pretending to be a traitor themselves. So, we meet Raphael and Ashtoreth* for the first time. And they meet each other, unknowingly. After all, neither ever met Aziraphale or Crowley. They don't have a clue that each isn't precisely who they claim to be.
This is the story of Raphael and Ashtoreth figuring out who is actually inhabiting the corporation they're interacting with daily. This is the story of Ashtoreth and Raphael's own relationship. This is neither a slow burn (Aziracrow), nor a quick seeming fast fall (BeeGees), but a steady almost human speed falling in love story (Raphtoreth? Ashphael?). The eventual determination of Ashtoreth to see the Real Aziraphale and Crowley freed versus Raphael's desire to stay in these corporations and be together themselves. Ashtoreth's eventual trip to heaven as Aziraphale while Raph is left to take the position of a bureaucratic denizen of hell with the small hope that they will be able to free the angel and demon they owe their love to and somehow, impossibly, not be caught themselves.
*The real one, thank you very much. They'd very much like to meet this Crowley who had the audacity to use their name for their own ends. But having incorporated both bodies and names eventually, they realize they really don't have a case anymore.
(The stipulations of the corporations are never expressly stated. Nor are there any details as to the ability to switch corporations between an angel and a demon. I'm basing the being caught aspect on the vagary of their respective exits from heaven and hell and what may have happened. We know that prior to the Aziracrow body swap, neither of them was aware of it being attempted because of the conversation about possession in the bar on the day of Armageddidn't. But, having been caught, heaven and hell are now aware of the possibility and immediately act to catch their own wayward traitors. Thus, Ashtoreth believes they are meeting Crowley at the swap and Raphael assumes Aziraphale is inhabiting Crowley's corporation. The lingering scents of heaven and hell would obscure the scents of an individual angel or demon in the immediate aftermath. How long before they figure out that there's an angel in a demon's body and a demon in an angel's body and neither is the one the other is sent to capture?
How long must they keep up the ruse? How long must they outwardly pretend to be ethereal and occult beings they're not? Because heaven wants answers and so does hell. Where are the traitors? Raphael must pretend to be Crowley for hell and themself for heaven. Ashtoreth must be themself to hell and Aziraphale to heaven.
Meanwhile, Ashtoreth is somehow also devising a plot to free the real traitors and Raphael, unable to convince them not to go with Metatron, is left in Crowley's corporation, to do their part (because they are as whipped as Crowley, apparently. Maybe there's something about these corporations after all?)
Oh, yeah, and the second coming is well, coming.
And Muriel. Can't forget Muriel. They know what's up from the get go because they are much cleverer than Metatron realizes (Ignorance isn't dim! Even if it was, they're still a being and deserving of respect! It's simply a lack of education and/or experience which Muriel rectifies quickly with their voracious reading! But they still mispronounce things or get things wrong sometimes. Elephants and Oliphaunts aren't cousins.), but they don't want Earth destroyed or AziraCrow punished either, so once everyone is in the know, they are as much an ally to Ashphael as they (I have no doubt) would be to AziraCrow.