In my experience, if you're twisting the body and knees at "not so natural angles" you are not doing judo properly. Form follows function and function follows form. Perhaps your natural angles are different though...
While it is almost certain that I do not do judo properly, what I mean to say is that most aikido throws are done from a "natural" hanmi or posture while judo throws in my understanding require to bend the knees and stick the hip out to one side while the torso twists the other way (as in a classic ippon seoi nage for instance). At least for me this is not exactly as "natural" a position as the triangular aikido stance and straight upper body from which most throws are executed. But again I might be doing it wrong.