For the calculations, I was thinking maybe one could cheese it a bit and get a relatively decent vague idea of the answer if not a more rigorous idea.
My vague idea was that gravity follows an inverse square law while the centrifigul force equasion is linear relative to the length of the tether. We know that gravity pulls toward Earth and the centrifigul force pulls away. So the net force on the weight at any one time is the centrifigul force equasion (a linear equasion) minus the gravity equasion (an inverse square equasion). We also know that the point at which that sum reaches zero is exactly the altitude of a geostationary orbit.
Work equals force times distance. So suppose we just took the area under the curve of that net force equasion from r equals the radius of the Earth to r equals roughly the furthest we vaguely guess we could send the weight before it starts to get sucked into the Moon’s gravity well. And then we divide that by the area under the curve from r equals the Earth’s radius to r equals the altitude of a geostationary orbit. That should at least give us a figure like “the amount of energy we could get back in theory would be roughly x times what it takes to get the weight past the geostationary orbit altitude threshold.”
The mass of the weight would be a term in that net force equasion, but if we just decided the mass was “one unit”, that’d make things a bit simpler. If we only care about the ratio of the energy we get back to the energy we put in, the weight should cancel out anyway.
This approach would certainly ignore a lot of things, but if the answer was “A Large Number™”, I think it would still be reasonable to handwave the details. (If the result was like 1.1 or something, probably “no, that doesn’t even work in theory” is the much safer bet. Let alone if it was less than 1.)
I guess if we wanted to get even more sophisticated, we could take into account things like the weight and tensile strength of carbon nanotubes and see if it would be infeasible to build a tether sufficiently strong without adding a huge amount of weight during the ascent. But I’d be willing to pretend in this thought experiment that we have some material with infinite tensile strength and zero weight at our disposal.
Anyway! Still not trivial math, quite, and definitely not terribly precise or rigorous, but not quite so “big-boy stuff” as modeling the rotational frames and such.