Why large-diaprhagm omnis? Small-diaphgragm omnis work great and, despite what you'd figure intuitively, will typically give you all the low end you need. True omnidirectional microphones exhibit no proximity effect, so there's no decrease in bass response with distance. If your kit is well-balanced and tuned right you can get a fairly massive sound with just an omni or two overhead.
As for the sound of the room, of course it helps if it's a good-sounding room, but even if it's not the best you can move the microphones a little closer to the kit than you might normally feel comfortable doing (again, because there's no proximity effect).
-Duardo