Let me just correct that there is a dispute among halakhic decisors regarding honoring a wicked father, and I wrote in accordance with the view of the Shulchan Arukh (Yoreh De'ah 240:18). In any case, according to most opinions, even if there is no obligation to honor him, there is still a prohibition against disgracing him. I repeat my recommendation to cut off contact.

A. Is this a case of the reason for the verse — an obligation based on gratitude (not ontic gratitude) plus the reasoning that recognition of the bad can cancel out recognition of the good?
B. Is there an internal halakhic source for using the reasoning of ontic gratitude (even if only as an interpretive definition of a Torah obligation we already know)? Or is there none, and there doesn’t need to be one?

A. I didn’t understand the reasoning. But this is a kind of the reason for the verse, as is common (a defining framework and not necessarily a reason).
B. There is a biblical source: “Is this how you repay the Lord, O base and unwise people? Is He not your Father, your Maker, who acquired you? He made you and established you.” There are two reasons for gratitude: He made you and He established you. But in my view this is simple reasoning, and no source is needed.

Thanks
[A. The reasoning I understood from your first answer is that ordinary gratitude is a kind of weighted balance, and if he did both bad and good, then the gratitude is canceled. Seemingly one could argue that gratitude stands on its own and recognition of harm stands on its own, like what they say about the World to Come, that a transgression (even if it extinguishes a commandment) does not extinguish Torah study.]

The meaning of the biblical illustration, according to what seems to emerge from part of Rashi’s commentary, is that the verse contains two parallel components — one value-based and one utilitarian. “A base people,” because He is your Father who acquired you; and “not wise,” because He made you and established you (it is foolish to bite the hand that benefits you, lest it become angry). “A base people” — because they forgot what had been done for them. “Not wise” — because they do not understand future consequences, that it is in His power to do good and to do harm.

With God's help, 8 Tevet 5781

Reason itself suggests that a person is obligated in gratitude to his father and mother, who gave him his life, and the obligation of gratitude for life itself is not nullified because of resentment over suffering or damage later caused by the one who gave him life.

Similarly, one should show gratitude to someone who saved his life for that act, even if later that rescuer caused him harm — after all, he is alive thanks to his rescuer, and for that he should thank him.

Even more so: even if the giving of life itself involved severe harm — for example, a mamzer, who from the moment he is born has that status — nevertheless the Shulchan Arukh ruled (Yoreh De'ah 240:18) that he is obligated to honor his father and mother.

With blessings, Yair Fishel Ordner

And perhaps even according to the Rema, who disagrees and holds that one is not obligated to honor his sinful father until he repents, it could be said that in this situation, in which he is not obligated to honor his father, for the same reason he is not obligated to follow the rulings of the Rema, which his ancestors accepted as practice. And consequently the ruling of the local halakhic authority, Rabbi Yosef Karo, applies to him — namely, that one is obligated to honor his father even if he is sinful. 🙂

I wasn’t discussing offsets, but by logic it seems that there is an offset here. Since I cannot repay him with evil for the evil, there is no reason to repay him for the good.
Nehorai, nice explanation. Some biblical commentators say as I do. If I remember correctly, for example, Rabbi Yosef Karo (the author’s uncle).