Upon closer investigation, I traced the car back before I got it, and got the following:
As I already knew, the transaxle had been replaced, though not properly, and that was corrected before I started driving the car.
As it also turned out, the engine had been replaced with a new one, apparently out of the box, and then the car was sold at auction. The really nasty oil I encountered when I bought the car, was break-in oil, most likely. Secondly, the oil I found after 1500 miles was like that because there was still gunk from the break-in in there somewhere. They changed the oil quickly.
Latest oil change reveals nearly invisible oil after 2000 miles, which is basically what I was looking for.
I got SUCH a good deal on this car!