@RogueTwo I contacted this professor after sending in my app. "Hey, I'm so and so and I have such stats. I do really relevant research. Please look out for my app."
I think it really helps that my advisor is pretty famous in his field. Gives my cold emails some weight. Got a Skype interview invite a few weeks later to "talk about my interest in grad school".
I'll give an update after my interview tomorrow morning!