How about this: "Dump" items off-map.
I support this idea, but I have a few questions,
1 Would you be able to retrieve said items if you were to 'go off map'. Perhaps in the stocks it would have a 'Landfill' section containing everything you threw over there, unforbid something and a dwarf brings it back.
2 would you be able to do this in caverns to?
You could theoretically have the off-map record of what has been dumped. When we get the "march units off-map" function of Army Arc, we might be able to see our landfill on the map, and send people out to retrieve something...
But again, if this is the equivalent of atom-smashing something, it's probably something a player wants gone forever, so I wouldn't think it a big deal if you couldn't get things back. You don't atom-smash the extra chairs you made if you left the mason on repeat for too long, you only atom-smash the stuff you know you will never need, have more than you will ever use, can replace at any time, and just want gone for good.
There's no reason to want to go back to the dump to pick up your 3,000 mudstone stones and 800 pig tail socks the goblins brought in that you can't even wear, anyway.
Garbage dumps in the caverns sounds... dangerous. I wouldn't want to send a convoy of peasant haulers into the caverns just to get rid of some junk. I'd rather take a relatively safe (provided it's not an evil biome) path overland. That said, provided the FBs aren't skulking about, it's possible...