For the benefit of any Googlers who are looking for how to do this, and for my own benefit when I forget:
Trying to get Conky to be transparent in KDE would either cause all my icons to disappear, the entire background to turn black, or Conky itself to appear entirely black. "own_window" and "own_window_transparent" and "own_window_type" in any combination didn't matter.
The answer is to go to Control Center -> Desktop -> Behavior and check "Show icons on desktop" and "Allow programs in desktop window". I was struggling for two days trying to figure this out.
EDIT: Strangely, I sometimes have to enable / disable this option in KDE, and then restart Conky, and THEN Conky will be properly transparent. Odd.