However, your big problem is propellant. For 1 kN @ 10,000 sec Isp,
you are using about 10 g/s. That means you have 100,000 kg of
propellant in orbit (expensive,

100 tonnes in LEO is indeed expensive, but doable with existing
technology, even if we don't revive Saturn 5 or Energiya.


probably impossible with the best propellant, Xenon),

This assumes, I think, an electrical thruster.

Maybe that's the right solution; maybe a mass driver slinging
sand is. That's part of the question.

and you are only pushing it at 1kN - so you aren't
accelerating very fast.

That's ok. Actually, that's where the run-time requirement
came from, though, admittedly, it kind of begs the question/
assumes something about the solution. Something that can
provide one to a few cm/s^2 would be fine.