stu,welcome to irv2
You can purchase flooring with the sub-base already applied to flooring its just a matter of laying the floor and allowing for expansion.
A 1/4" is required around perimeter of floor and you will have to place a new mopboard if the one you have now can't cover 1/4" space they have for floor color and type.
As to a slide they have dress moldings for finishing edge of floors if you were to dress each edge with this molding it may work. There are different types of dress moldings you would have to match which would work best for you with type of slide you have so it will stand up to the slide traffic running over each floor layer. These type floors are floating floors and not glued down its what you would want anyhow because of the flexing 5th floor.
Take your time think it out and I tkink you will be proud of your job when completed.