One more thing, NEVER LOCK ANIMALS IN A ROOM.
They hog frames trying to calculate a way out of the room even though they can't.
Ah, got to be a little more specific than that or you'll give people the wrong idea.
The problem is that if you forbid a door to animals ("tightly closed"), and the animal wants to get past the door, it will constantly check the path even though there is none (the door is forbidden to them!)
Blocking them or locking them in by any other means (bridges, L-forbidden doors, etc) is perfectly fine.
they're dumping it into magma and creating possibly thousands of "ghost-globs" due to a glitch
Unless you mean "ghost" items that won't even show up on the stock screen (which would be a new phenomenon to me), I don't think I've ever seen more than 2 figures of them for every couple thousand stones melted in magma.
Now if I did want to make sure I dumped stuff down a chasm as opposed to into magma, would flushing my garbage work? I'd like to avoid having my dwarves carry garbage all the way to the chasm, which is usually going to be outside my main shaft, so having a way of conveying it towards the chasm by mechanical means would be helpful.
It's a glitch; it's not consistent. You've just been lucky. Dumping items into a magma vent where they will fall off the map if the dump is well-placed is a common successful tactic as well. It's just equivalent to using a chasm.
Items will be flushed by a high enough water flow, but I don't really know how DF handles it. Maybe someone can tell you what would be necessary to get heavy stones to flush a significant distance, but I'd imagine it would be considerable. You can drop them off the map through underground river exit tiles as well, of course.
The thing is: the best and most convenient way to get rid of unwanted items is atomsmashing, period. You can build your one-tile atomsmashing bridge anywhere you want, so the hauling distance can be whatever you want it to be. You can build as many of them as you want. And you can build the lever(s) wherever you want.