I like to say that we're not in the information age, we're in the
energy age; taking the name of the age from the limiting/defining resource for techinical and social expansion as we have since the bronze age forward.
in a gravity well, matter is plentiful, and energy is the limiting factor.
in space, matter is the limiting factor; once we're firmly ensconced in space, then we'll be (probably) in the aluminum age.
back (sorta) to topic:
Dropping aluminum and hydrogen down the gravity well and shipping the oxides back up for reprocessing would work excepting for the huge energy penalty for the up-bound trip. . . the energy required to orbit mass from earth far, FAR outhweighs any energy that could be garnered from using the aluminum as a energy source.
However, it is an interesting way to get oxygen into orbit in an inert form, and might off-set some of the orbital insertion energy penalty if we left it there.
One question: where does the hydrogen/water come from that you're breaking down in orbit? the solar wind, i suppose, but have you stopped to consider the energy cost in collecting the solar wind without being 'blown' out of orbit? The only other place I can think of would be cometary ice- with obvious practicallity issues involved with recovery. The supplies of water on the moon are only conjectured and would be a finite resource better suited to leveraging moon habitation (should we choose to undertake that) or outward bound exploration. The water reserves on the moon, even if the energy cost to get them into LEO were negligable, would be insufficient to make even a small dent in humankind's thirst for energy. But, because electrolytic separation of water is easy to undertake, it becomes a stepping stone to industrializing space.
to modify your scenario a bit (the following still fails the economics test, but it's closer. . . lift one or more energy producers (fission, fusion, PV, solar concentrator, antimatter, trilithium, unobtanium-zero-point-resonance-reactor, who cares) onto the moon.
Mine the moon for aluminium oxide and any mineral hydr-, carb- or nitr- -ides or -ates that might be present. Process those materials and capture the light elements for lunar use, or combine them into water or other compounds for shipping convienience and send them up to the L-point where they could be used for farming or separated for fuel/reaction mass, or even (gasp) breathing.
Form the aluminum into coil-gun or railgun projectiles, with more valuable cargo embedded, and fling them into one of the L-points for use in space industry.
(The moon has a lower 'escape' velocity and no atmosphere, so magnetic launching from there reaches the ragged edge of feasability.)
Loft some alumina-based foamed ceramics heat shields, too: Any material excess to requirements for shipyards/habitats/powersystems/industry in the L-point gets mated with a heat shield and pushed via ion engines to a re-entry vector and left to drift 'home'(say, the shallows off the US/Mexican Gulf coast or perhaps potions of the Mediterranian or the western pacific) while the robot-guided ion tug returns for refueling and a fresh load.
The potential for terrorism here is high; imagine the fun a 'cracker' could have 'throwing rocks' at cities or countries he took a dislike to. . . with no parachute, you'd have incandescent multi-ton projectiles at trans-sonic speeds. not a good thing to have landing in your city.
Due to the thermal and impact loads, shipping finished goods down would likely be impractical; but with a presence in space, the follow-on to the shuttle could be used to de-orbit more sensitive cargoes.
the payloads get recovered and parceled out according to the highest bidder; if using the aluminum as a 'fuel' were a desired outcome, then there you go.
at least in this scenario, the gravity equation is positive instead of zero-sum. . .
I make no predictions about environmental effects in the impact zone/s. . . undoubtably, there will be some rare organism there that needs protecting somehow.
