I absolutely would raise its stats. It is a totally changed creature--not just physically but mentally. Its alignment fades away into a neutral single-minded drive for revenge, it gains supernatural immunity to fear and charm, as well as resistance to psychic damage. It has a mystical sense of the location of its quarry. Plus, the text implies it is somehow imbued with divinely sanctioned power. Allowing its single-minded purpose to grant it a single-minded focused reasoning ability (Intelligence), its supernatural awareness and power to increase its perceptiveness and willpower (Wisdom), and its unrelenting sense of purpose and divine powers of retribution to increase the intensity of its presence (Charisma) seems highly appropriate.