Oh, my apologies - that was my coffee-extruded first-pass, in the hopes of any curious or knowledgeable feedback, and I guess I shot myself in the foot by being imprecise :o
Specifically, if you have a roll of saran wrap straight out of the box, and you re-roll it, same arrangement, onto your hollow (aluminum?) axle, then you've done a single re-spool.
Now, to complicate that process: in-between the spools, put a roller with narrow ridges routed to follow along its length, like a churro. Conductive ink, brushed onto that roller from above, is pressed onto the saran wrap as it is being re-spooled. Those lines of ink will be parallel to the axle, running like a tree branch's fibers, and as you roll the saran & pin-stripes onto the axle, your conductive ink forms many tiny, insulated capacitors. Put the two spools far enough apart to have a drying-fan segment, so you don't have to roll slow.
Once you have a desired depth of 'solenoid', stop rolling, and ionize the ink-lines from the exposed edges (the ink-roller went right up to the edge, or you lop-off the nubs to expose the edges). The capacitor lines are all 'wired' by a ring or collar and cap that they touch, so it's a massive parallel array of tiny capacitors. In most circumstances, you would charge it up a few minutes before you plan to be using magnetism, otherwise the capacitors do slowly leak. Heavy-duty carbide-slug vacuum capacitors would avoid this problem, but that's for a navy-destroyer-type budget.
With the axle on a low-friction stand, a belt to a motor off to one side, you should be able to power slugs of iron with almost complete transfer of force from the motor's torque into projectile or chain. Mining gets a lot easier, because joules of *shock* are much more efficient for crumbling brittle rocks, compared to joules of *scraping* . This also avoids needing to maintain the cutting tools - no contact with the projectile, and the projectiles are just amorphous lumps of iron, pressed and re-used.
Fundamentally, this is like the mental block we usually have about 'joules to transport a ton a certain distance' => technically, any point on the same topographic line as you *should* cost zero energy, but we always assume the enormous resistances of the real world. Wires pumping electric current produce a similar resistance, and that's what makes normal solenoids so weak and costly to operate. Physics doesn't demand that "making magnetism should always be wasteful" - it was just the resistance, heat, impermanence of making magnets with an electric *current* that was the problem!
Thank you for considering this - I am a tiny-apartment mathematician, and people with garages and tools, the explorers, are the bridge to reality. It ain't anything until it exists :)
[Oh, and as far as I can tell, the best budget carbon ink is from Robert Murray Smith - just google his YouTube channel, full of his stuff... I was going to contact him once some physicists correct my assumptions.]