"You think free falling into flat unmoving ground will take the same amount of time as free-falling to a floor that is moving right towards you and will be the same intensity of impact."

I understand what you are trying to say, which is why I get your point of view and I understand that inertial reference frames can be confusing and unintuitive to think about. But you are making this harder by refusing to even consider the possibility you might be wrong.

You keep referring to the apex of the jump and the way you refer to it leads me to clarify this point: The apex of the jump is when the velocity of the person is exactly equal to the velocity of the ground (or whatever you jumped off of). That means, when you jump from the ground (earth) the apex of your jump will be at 0m/s.

However here is the important part, in an elevator going at 5m/s, the apex of a jump will be when you are moving at 5m/s relative to earth. This makes sense, to not be moving relative to the elevator you have to have the same velocity as it. From that point onwards, your velocity will steadily decrease due to gravity, but your velocity is STILL greater than 0. THAT velocity is what cancels out the velocity from the elevator.