I struggled with the cool plate while printing bambulab matte PLA. It stuck too much to the plate, especially the initial traces.
I just realized that the hot plate sticks just right! Just sayin’ in case it helps someone else.
PLA on the cool plate, without glue is too sticky. If you use a glue stick and spread a thin layer on the plate you’ll get a good amount of adhesion but not as sticky as what I think you are experiencing.