Heck yeah. Have myself a bag of PhD complete as well and excited to see what it can do. I have always wanted to aerate my lawn. To me that’s some next level stuff. I’m getting there. Ha! Keep up the good work man.
I would have left the cores down. If you did an overseed and fert the cores would break down and add to your soil. Just a thought. Only reason I say that is because golf courses do it every year and I can imagine the work to get up all those cores.