Most people only know about Kartavirya Arjuna as the thousand-armed king who was the villain of the story of Vishnu's incarnation Parashurama. Kartavirya Arjuna stole the divine cow Kamadhenu from Parashurama's father Jamadagni, so Parashurama cut off his thousand arms and killed him. In response, Kartavirya Arjuna's sons killed Jamadagni. To avenge his father's death, Parashurama annihilated the Kshatriyas of the Earth, who had become corrupt, 21 times, as I discuss in this question.
But my question is about Kartavirya Arjuna himself. I had always considered him purely as a villain, but then I found out the Narada Purana has two chapters devoted to various mantras to Kartavirya Arjuna, including a Kartavirya Gayatri mantra, a list of 108 names of Kartavirya Arjuna, and a Kartavirya Kavacham, analogous to the Narayana Kavacham (which I discuss here)! The reason for this seems to be that Kartavirya Arjuna was actually an incarnation of Vishnu's Sudarshana Chakra. Here is what this excerpt from the Narada Purana says, for instance:
He was the incarnation of Sudarshana Chakra on the Earth. After propitiating Dattatreya he attained excellent brilliance.
And here is what Vishnu tells Parashurama in this excerpt from the Upodhghata Pada of the Brahmanda Purana:
Indeed Kartavirya is the incarnation of my discus, on the surface of the Earth. He has finished his assigned task, O excellent Brahmana. Finish him, O bestower of honor.
And this later excerpt from the Upodhgata Pada of the Brahmanda Puranas describes what happens after Parashurama kills Kartavirya Arjuna:
The king who was a devotee of Datta, entered Sudarshana, the discus of Vishnu. His body became reduced to ashes[.]
So my question is, why did Vishnu's Sudarshana Chakra incarnate as Kartavirya Arjuna, an enemy of Vishnu's incarnation Parashurama?
The only story I have come across (given in this webpage, for instance), goes roughly as follows: The Sudarshana Chakra become too arrogant, and brags that Vishnu is only able to achieve his great deeds because of the Sudarshana Chakra's help. So Vishnu curses it to be born on Earth, saying something like "You will be born as a powerful king, and you will have the same thousand arms that you currently have. I will be born as the mere son of a sage, and I will defeat you."
But are there any scriptures that describe this story?