A few(+) hours of TLC on Ruthie's KDX and it seems to be running much, much better. The previous owners had the carb all fuckered up. The Pilot Jet was completely clogged, so to overcome the bike's inability to idle, they'd simply turned up the idle screw. This forces the slide to always remain open more than at should at idle, completely throwing off the jetting. I also found the throttle cable to be so poorly adjusted that not only did it not have any slack, it was actually holding the throttle open in addition to the turned-up idle screw. Idiots.
The silencer was thoroughly packet with spooge and was quite likely not flowing very well. I drilled out a few rivets to completely disassemble it, clean it out, and repack it with fresh material. I was also able to hammer out some dents in the tail cap.
Now it's starting to run like a good KDX should.