Plate compactor is the only way to go in this situation. I would still be hesitant about trying to compact that dirt. Undisturbed soil is what is recommended, just imagine how much pressure was put on that undisturbed soil over the ages, that is why they want you to do it that way. Use caution, even if you tamp the living "you know what" out of that soil, I wouldn't be surprised if over time you start getting some unevenness in the soil, which could cause you major headaches down the road. Take the time to do it right the first time and you will have a much more enjoyable time actually enjoying your pool. IMO I would get some paver base, put that down, tamp, water, more base, tamp water etc until you get it perfectly level and it is hard as concrete. Good luck. Post pics.