Above Ground Pool Install - Removing Stumps

Hi - I'm new to the forum. I tried to search this before I posted the question but until I post a question it will not allow to me search. I hope I am not beating a dead horse!!

I am about to install an above ground pool. 15 x 30 Oval. I need to remove some trees where the pool will go. I understand that I need to remove the stump entirely as they will decay and cause a sink hole in my pool. I have a backhoe so that is not a big deal. My question is about how to fill in the hole. I understand that (ideally) you want to level your ground from the lowest point, however, a pine tree tap root can extend 15 feet into the ground... How do you suggest I fill the hole to avoid settlement issues later? I also have a plate tamper at my disposal..... Many thanks for this ABG newbie...