I've talked about this quite a few times on the Beyond Canon discord, and the theory I have is the common one over there:

Bard of Doom Tavvy

Thief of Mind Vrissy

Mage of Rage Yiffy

Sylph of Blood Harry

Ordered by descending confidence in my belief that I'm right. Though, I'm fairly confident in my aspects.

All 4 use the aspects which went unused by the humans, as you would expect. Furthermore, all of them contrast against their parents' aspects in some way. Tavvy has the opposite of his mom's, Vrissy has the Pyrope aspect instead of the Serket aspect, and Harry has the opposite of his dad's. Yiffy's doesn't contrast, though frankly I think her being left out of the pattern fits her role in the story (and considering that she's inevitably going to break the pattern of the AG/GG/TG username scheme, has some basis in canon). I wrote about this a while back on a tumblr post (which I'll be copying some of), though I had Harry and Yiffy's classes swapped. I still could swap them, but I'm leaning more towards this setup atm.

For Tavvy, I say he's Doombound because of him being the Crockercorp CEO's son. Being in that position, he's been put onto the side of the organization/empire that's brought most of the suffering and conflict currently encapsulating Earth-C. Tavvy's whole attitude also has an aura of 'doom and gloom,' to it, even in comparison to the original Tavros Nitram. Also, it should be noted that him being Doombound would be an interesting subversion of Jane & Meenah, the previous Crockers, being lifebound.

I say he's a Bard because he goes against the Doom-full situation he's been stuck in, albeit in minor ways. He's allied with the resistance, and is dating the daughter of one of the main resistance leaders. And despite him not being the most optimistic, he doesn't let it show too much.

Next is Vrissy. Firstly, I would like to mention that Vrissy has not once been shown bearing the Scorpio sign. It's nowhere to be seen on her outfit, and when she texts someone her face is used instead of any symbol. As such, there's nothing tying her to Light, Despite Vriska and Aranea both being Lightbound. Considering that this story has gone out of its way to never associate her with Light, I believe her aspect is something else. My best guess is Mind. I say this because unlike Vriska, who's usually going straight into things without a plan, Vrissy consistently comes up with a plan before taking a step forward, though given that she's still a Serket, this usually results in her arguing with her friends while trying to make said plans. Finally, Vrissy being Mindbound makes her a Serket with the Pyropes' aspect, while her being a thief shows some inheritance from Vriska.

The previously mentioned arguing is also why I say she's a Thief. She's the one making her partners go through impulsive shenanigans for her, may it be to hide a body or to crawl through a window for a makeout session. Also, her improved Vriska mind control abilities enable her to literally steal minds.

Yiffy being rage doesn't need much explanation. If you need one, refer to BC Page 562 (https://beyondcanon.com/story/562) and compare it to the Extended Zodiac's Rage description (http://hs.hiveswap.com/ezodiac/aboutaspects.php). I really think this just speaks for itself.

As for her aspect, her teen angsty know-it-all nature regarding the way to world works fits with the idea of her being a mage (assuming that they're the active equivalent to Seers, which is very plausible given them being likened to prophets multiple times). The alternative could be her being a Sylph who spreads Rage, but I don't think that fits her. Though, arguably it could be given to her because she'd hate being the magic fairy class.

Lastly, Harry. he's described as a "social climber," in the patreon commentary of the page where we saw his phone, works with others for musical plays, and appears to be the person who's most into the celebrity-esque role thrust onto him by his literal-son-of-god status. He also appears to be closer to his parents than the others are, or at the very least talks about them more. Being bloodbound would give yet another candy kid an inversion of their parent's aspect, as he's the opposite of John's Breath. Lastly, I want to add the anecdote that when Vrissy makes fun of Tavvy for his genocidal parent during the pre-hiatus run, he's the first person to say that it's not cool to bring Tavvy down for that.

Harry being a sylph is a bit odd, given that he'd be the only one here who doesn't align with his class's gender (I know class genders are a bit iffy but I'm assuming that they'll still have some presence, just not an outright defined one). With that being said, I think it fits him. Sylphs seemingly heal using their aspect, or at least spread it for the benefit of others. Harry's tendency to vouch for his family aligns with this. It doesn't quite fit the "social climber" aspect in the same way that Mage does, though. Also given that he has a major interest in theater, I think giving him the magical fairy class with consistent parallels to the Peter Pan would fit him.