Understood. (Interesting, your interface is different than mine - I don't have the horizontal slider, only the vertical one).
At any rate, you are referring to relatively small safe areas. My problem seems to be larger. Here is what I get when I load the models into Cura (before any slicing is done):
After slicing, with layer view / first layer as you guided me, this is what I get:
Obviously, the six grey pieces are not sliced.