Thinking outside the slab one solution would have been installing rigid insulation under the slab turning it up on the perimeter to form a giant pan and then casting the concrete slab inside the pan.
Rigid foam under subfloor.
The right kinds are even dense enough to support a plywood subfloor without any supporting wooden strips underneath.
Tape the seams of the foam panels with heavy duty construction tape.
Rigid foam is a nice option because it provides an excellent thermal break between concrete and flooring.
Lay sheets of high density rigid foam over the polyethylene.
For the pool table you will still float the floor normally.
You simply lay sheets of foam on the basement floor then fasten 5 8 plywood on top with concrete screws driven into predrilled holes in the floor.
Leave a 1 4 inch gap around the perimeter.
Foam board insulation is used on attics and walls yet it can also be used to insulate your floors.
Rigid foam insulation.
But insulating your floors is a good idea for many reasons including energy efficiency and height adjustments.
Lay rigid foam.
Unlike above grade sub flooring basement sub floor has to do all of the usual things and more.
Since the weight it distributed throughout the 4 legs it will still be able to float normally.
The top layer of subfloor steps back and gets a layer of peel and stick flashing tape to form pan flashing under the sliding doors.
With a rigid core plank you can add additional underlayment under the planks however i would keep it at 2mm or under.
Rigid foam makes a great basement floor insulation.
The other was 2 of blue foam over a concrete slab with a layer of 2 x2 squares of osb with plastic dimple board as a floating floor over the foam.
Basement subflooring has so many jobs at hand.
Most people do not think about insulating their floors unless perhaps it s their attic floor.