P.S. I exported the model as STL from 3D Builder, and opened that STL 8 times (instead of multiplying it). Now I tried importing 3MF directly from 3D Builder to Cura (and multiplied it there). That set is sliced OK, so I can continue my work now.
However,although the problem was apparently in the model, why were these 8 objects sliced so differently? I mean, especially, 0.4 mm thick solid block in only one adjustment screw is not a small glitch. Plus the three others with a single solid layer in the bottom.