Seems like a bit much for me... I think that the concept of Mrs. Cartman also being Mr. Cartman is WAY beyond the scope of even South Park reality. If you considered the possibility of artificial insemination (which is how you appear to have come up with her being the pops also), that would not make her the dad... Just a single mother.
You did remind me of something interesting. Someone (don't recall who, though) posted that it might be Tom Selleck (as a result of the Anal Probe episode and Eric's comment). That seemed like a very feasible answer. However, you do bring up a very good point. Tom wasn't in the room.
My guess would be Ned... Just seems like it's too good a thing to pass up.
Suppose we'll find out soon enough, though...
Later, Adam