Holy. Crap.
So, apparently we had some magic erasers around the house already, so I pulled the shell off the eMac, used some high-pressure air & Q-tips to clean out the machine. Then I got to working on the shell.
First, I put it in the shower and used the detachable showerhead to wash away all the caked on dust (which seems impossible to actually clean entirely under the clear plastic grille, as the grille doesn't seem to come off). Second, I wiped the thin film of sooty dust out of the inside of the shell. Last, I went at the 20 or so brown & black scuffs, marks, and dings on the outside of the shell... the Magic Eraser is... UNBELIEVABLE!
The eMac looks practically brand new! I need to get some NOVUS #1 to get rid of the swirl marks and bring everything back to its showroom glow, but as-is the Magic Eraser treatment absolutely blew me away.