"Yehuda HaLevi, Rav Hirsch, and Rav Kook all viewed evolution as the mechanism used by G-d to produce the animal kingdom."
To my knowledge Yehuda Halevi said no such thing. Even according to Dr. Aviezer's paraphrase, which has no citation, Halevi says the simple was created before the complex. Creationists do not and need not dispute that. Kuzari is also clear that Adam is a special creation and the origin of humanity less than 6000 years ago (1:4, 2:14).
Rav Hirsch never said evolution happened. He said evolution if established as truth would not contradict the Torah. Even assuming he would have been convinced by 21st century science, that is not proof for Dr. Aviezer's claim.
I believe Dr. Aviezer is correct about Rav Kook.
I have seen Rav Soloveitchik's writings misused in support of creationism. Evolutionists too need to approach sources with care.