Just hold a trouble light in one hand and a screen sander in the other hand to sand down the joint compound. The sharp angle the light will be hitting the wall will exagerate the bumps and the valleys giving you a much better idea of where you have to add joint compound and where you have to sand it off to make the wall smoother.

Slip a green Scotchbrite pad under the sanding screen on your hand sander. The sanding dust will go through the sanding screen and fall out of it's edges through the Scotchbrite pad.

If you want, hold your vaccuum cleaner hose under your hand sander as you tap the hand sander against the wall to knock all the sanding dust out of the Scotchbrite pad. Use a 60 grit sanding screen so that you make fast progress, and the joint compound you sand off is in large enough hunks to fall directly to the floor without spending any time getting there. The vaccuum cleaner will collect 90 percent of the dust before it hits the floor.

Wipe the wall down with a dry rag or brush after you finish sanding, and then vaccuum up with a wet/dry shop style vaccuum cleaner fitted with a pleated paper filter. It will NOT take you even a day to vaccuum up, let alone "weeks". It's really not anywhere near as hard as you're making it sound.

Also, you should be aware that there are different kinds of joint compounds.

"Regular" or "Taping" joint compound has the most glue in it and is used for taping the joints. The glue in it makes it stick better to the wall and the tape to stick better to it, but that glue also makes it hard to sand smooth.

"Topping" or "Finish" joint compound is used for the 2nd and 3rd coats over the joints, and has the least amount of glue in it. That makes it very easy to sand smooth.

"All Purpose" is about half way between Regular and Finish. It can be used for both taping and finishing, and it's made mostly so that drywall contractors don't have to carry two pails around in their truck with them everywhere they go. They can do the whole job with only one compound.

Your best bet is to buy regular joint compound for your first coat (which you won't be sanding) and allow the compound to shrink as it dries. Then, use Finish joint compound for the 2nd and 3rd coats, which will be easy to sand smooth. And, hold a trouble light close to the wall so that you can see when the joints are smooth, or where they need more joint compound, or where you need to sand more joint compound off. When your wall looks "not too bad" when viewed under such critical lighting, it'll look perfect under normal lighting.