I find this last bit short-sighted.
The solar system is large enough to dedicate a trojan point to waste consolidation.
I fully believe, once we get nano-assembler technology figured out, WasteManagement may become one of the richest MINING corporations in the world.
All the elements you need for civic live, all collected in one spot: your local landfill.
When we get nano assembler technology sorted out, nobody is going to notice a few million metric tons of rock when we can dismantle MOONS. Or turn the planet into a solid ball of infinitely recycling nanomachines thanks to a gray goo scenario.
You don't dig for gold in an iron mine. No point in throwing it beyond our reach if you don't have to, and so long as the possibility of recycling it might become cost competitive in the not so distant future.
Again, the solar system is vast. Putting it in one place to mine later, (assuming cheap intra-system drive) makes more sense than putting it on a terminal orbit around the sun.
What's easier though, parking millions of tons of rock in a Lagrange point, keeping their masses from interacting enough to throw one or more out of it, in the hope that itll become useful at some point in the future, or dropping a nuke on one that kicks it in the general direction of the sun via a nice, predictable orbital arc? There's NO shortage of crap in the solar system to dismantle at the molecular level. The Oort cloud accounts for almost as much mass as the rest of the solar system *combined*, and it's far easier to corral in bite-sized chunks should there be any need for it.
And if that rock does not contain gold, or iridium, or some other rare element (just about anything else heavier than iron), you're SOL.
If memory serves, the elements heavier than iron are formed in planetary cores, so debris from stars is significantly lacking in those elements.
For truly long-term planning, don't throw things away where you can't recover them.
Though I think I'd pick out a couple of large stoney asteroids and use those for a core to hold the garbage pile together.
OTOH. simply weld the iron shipping containers together.
Gripping hand, inflate a nickel-iron asteroid and stuff the garbage inside.
BTW, this type of recycling is already being done . . . many of the ancient metal mine-smelter areas are reworking or have reworked the ancient slag for metal with newer technology that's better adapted to low-concentration ores than the ancient techniques . . . in some cases, too-rich ores can poison modern refining techniques! And this has been going on for at least 250 years!