"Work done = force x distance moved" tells you the work done by a
constant force. If the force is varying, you'll need to use integration on the RHS, to find the work done.
Also, I'm not clear what force you're refering to here. You're posts are rather vague with the details.
From an energy consideration, the EPE will equal the loss in GPE in going from their starting position to their first stationary position (since the velocity will be zero in each position, the KE doesn't come into it).
The force in the rope is varying as the rope is stretched, so you can't used "work done = force x distance moved".
For EPE, you have work done in stretching the rope
=2lλx2 for any given extension.
You also have
F=lλx via Hooke's law, again for any given extension.
Those are the two formulae you should be comparing if you're going to do it that way.
Note: The extension of the rope is not the same as the distance fallen.