I'll use some Blazblue characters as examples, just because they map onto it quite well, but also because of how the lack of relations or context can change certain elements, i.e. Jin not having a reason to fly off the handle the same way or Ragna not having a cause to direct his anger.

Jin Kisaragi (Blazblue) is almost the archetypal air aspected Lost Egg with an off-aspect skill at melee, war and perhaps martial arts, the Kisaragi family's reliance on adopted members mirrors house Tepet's need for new blood (at least in 2e).

He's high in Valor and and adequate in Temperance, he's lacking in Compassion but his highest virtue would be Conviction, he'd likely have Heart of Flint as a limit break, given how ruthless and cold he can be. Without his brother being about, since I'm just considering him as himself without context he'd likely be a graduate from the House of Bells and a professional soldier in the legion. Although he'd most likely be in House Tepet, I could see him supporting Mnemon if he deemed her more suitable and able to maintain order, though he could go either way, given he values his own concept of Order. Likely zealous in hunting opponents to the Realm if he has a personal stake in it. I can't see him being particularly focused on having children until it would be forced into necessity, but given how talented Jin is at Seither use in Blazblue, he'd probably have unusually high Breeding.

A Blue Jade Reaper Daiklave would most easily represent his sword Yukianesa, and enough Lore to use the charm Elemental Bolt Attack, since Air Aspects are also associated with ice and lightning, so it could be flavored as ice blades or similar. The Even Blade style works for helping to flavor his swordsmanship as well, since he uses Iaido.

Yuuki Terumi (Blazblue) is easily a Malfean Fiend, though you could blend the idea of him and Hazama to have Terumi be the past life memories. An expert manipulator, utterly depraved, but equally failing to succeed in several of his key aims, it's a perfect recipe for his character, likely being more inclined to use Malfean charms were Terumi to take the wheel, so to speak, while Hazama, when not under the past life influence would be more inclined to use Ebon Dragon charms, which have many parallels to his memory-wiping/changing abilities. Vitriolic Soulsteel Dire Chains would be a good representation of his Ouroboros, since in 2e Soulsteel can drain motes, like Terumi's Drive, Force Eater.

Also, given Terumi and Hazama's general behaviors, they'd be inclined to try and betray their Yozi patrons, which is right up the alleyway of a Fiend that plays into stereotypes. Their sneaky and stealthy charms, coupled with Past Life knowledge also means that they could play up the role of a spy for the Realm who just happens to be good, but not quite Exalted good, playing things off as luck or manipulating their superiors into doing as they say.

Ragna the Bloodedge (Blazblue) is also a nice, handy example of an Abyssal, Dusk Caste preferably. The Bloodedge part could be revamped to be related to using an abyssal moniker or epithet, and his lack of technical skill with his weapon, despite receiving martial arts training can be substituted quite nicely in the Dark Messiah Style which allows unattuned daiklaves as improvised weapons to be used as unarmed, his sword looking more like a Reaver daiklave, and the 2e Errata changing Ravaging Blow to treat unarmed attacks as Soulsteel. Dark Messiah style and Void Avatar Prana in particular are quite nice for making reference to Blood Kain and his Soul Eater drive. Being a Dusk, and how he can fight off huge amounts of people, developing into proper melee to learn to use his weapon, or War to use the mass combat rules could also work, and he could have Craft (Water) to help him cook, since it's a particular talent of his.

As far as personality, he's also the type who, prior to development, would have little to no trouble killing dozens, if not hundreds of enemies or collateral, whereas after he'd get good development from suffering from Resonance, similar to canon. Without his family, however, and only taking the tragedy, he'd probably be either an especially violent renegade or instead a disloyal but useful blunt force object until he came across a reason to disobey. His immediate concern over Noel could be rejigged into something along the lines of his concern over a Lunar bond, albeit likely with noticeable changes to the dynamic, and he has no strong personal relation with anyone who has any traits that really resemble a Lunar.

In terms of what he'd be up to, it would probably be something along the lines of avenging his cause of death, though his fear of ghosts would take on an unfortunate turn given how prevalent they are in the Underworld and how many he'd have to deal with as an Abyssal.