When I looked at all the bottom surfaces of printouts, there was a very noticeable pattern there! Look!
The places that were stuck the best were the same on all parts.
Most of them (except two, from the first black batch) were printed with high voltage off. That suggests that when I had high voltage on, the surface was indeed seriously affected. And that's less and less surprising..
To get best results, I cranked the high voltage as high as it was possible - to the point the extruder-bed gap was sparking occasionally. And the dotted patterns suggest that the sparks were a big player here.
I even noticed some plastic residue on the bed itself. That is, it was stuck to the bed there so well, better than the plastic sticks to itself. Fascinating!