Yeah, it doesn't really matter whether the sub is down-firing or not - as may have been mentioned here by others. You issue is that the subwoofers soundwaves are going to couple with the floor and walls and such, and translate out to your neighbors. Yes, some of the sound will actually pass through the materials and into the spaces as well.
Putting more insulation will help a tad bit for bass, but not enough, as bass waves are long - and you really need to put serious mass between you and any other zones, and/or "de-couple" the boundaries!
You could build almost a complete floating floor over your existing one, which will help quite a bit in keeping the bass down bellow significantly. However, the walls still attach the floor, which should have issolated walls to be more completely effective in your effort - and there are alternatives here, depending on how involved you want to, and CAN get.
If it were me, and I lived in an apartment, I would simply be satisfied with some larger bookshelves that played down to the high 40hz range, AND FORGET ABOUT IT!
Really, it's all about quality anyway. Small speakers do well in small spaces - set up well. If you had a large space that would support such a beast, then fine. You live with neighbors all around. So I would be happy simply considering them, and just enjoying what I have, personally. But, you might be coming from a different place.
I say this, as I really used to enjoy going over to a friends house and listening to music and movies on his really nice monitor system, 2 channel! (sans the sub).
Perhaps you could do some reasearch on sound issolation on the cheap? Hummmmmm....
How about this - you go on craigs list, and look for some office particians that someone is giving away for free, cause they're moving buildings or business's or something! Then, you use those as your floating floor base, as well as side walls!!!! That would work! Lol- you might have to firm up the pannels in places, like the floor. But hey!..they'd be free!...
It's a thought
good luck