I think Voq is The Albino from the DS9 episode Blood Oath. This started out as one of those out-there ideas, but the more I thought about it the more it made sense, especially with something from Butcher's Knife. So how do we get from the idealistic and principled Voq to the brutal child-killing Albino? Quite easily, actually.
Let's start with what we know about The Albino. We know he's an outlaw of ambiguous species, but implied to be Klingon. We also know he killed the firstborn sons of Kor, Kang, and Koloth. If he is Klingon, then judging by his makeup he's probably about the same age as the trio. This is where it gets interesting. Kang's son was named Dax, after Curzon Dax. The trio met Curzon when negotiating the Khitomer Accords. This means that The Albino killed their sons after they created an alliance with the Federation.
Now let's go to Voq. Voq is fanatically loyal to T'Kuvma's credo of 'remain Klingon' and is similarly fanatically against the idea of peace with the Federation, to the point of refusing to salvage supplies from abandoned Starfleet ships. Voq now also has a grudge against Kol, who has been confirmed to represent House Kor in the Council. I assume that Kol is likely Kor's younger brother and they're set up like how Worf and Kurn were when their House was restored to the Council. Kol defeated Voq not through combat, but through deception and bribery, an extremely dishonorable method by Klingon standards.
Now let's connect the two. In Klingon culture, the sins of the father pass to the son. Additionally, crimes committed by one dishonor their entire House, not just their descendants. In Voq's mind, Kor may well be equally guilty of Kol's transgressions as his brother and head of the House, providing early conflict between the two. Now let's assume that Voq doesn't win and never becomes the Chancellor of the Empire. Not exactly a stretch. Having lost, he would have become an outlaw and gone to ground. Decades later, he learns about the Khitomer Conference, and how his old enemy Kor, along with Kang and Koloth, are negotiating a peace with the Federation. This is exactly the thing that T'Kuvma was worried about and adds to the list of dishonorable actions Voq attributes to Kor. They and their Houses are now traitors. Since their children are considered equally guilty, and they're easier to kill, that's who Voq targets.
I'm sure at least one of you is thinking, "Surely there must be more than one albino Klingon out there?" I thought about that and absolutely, there must be more albino Klingons somewhere. However, there are two points in my favor here. First, in Voq's introduction, it's implied that albinos, and possibly others considered deformed, are often killed at birth. Second, Voq and The Albino are about the same age. So, in a society that kills albinos in infancy, the odds of there being two separate prominent albinos born at roughly the same time are slim, at best.
And that's it. That's how I think Voq will become The Albino.