Any way you cut it, that's an incredibly heavy and complicated set of stairs. It would be much lighter, more compact, and more reliable (and probably easier and cheaper) to build a complete new set of stairs that fold out of that hatch.
If you start with something like these scissor steps, recess the top bracket in the floor, and notch the door (with good weather stripping), you would be able to open the door, fold the stairs out, and close the door again.
Scissor steps