You are a bit screwed in trying to automate this I think... The reason I could see for the 3 depths, is that you have "flat area detection" turned on. With that, rotate your model a bit, and you will see that the 2 extra passes correspond to the shallower grooves that are in the plate. This is unfortunate, because you are not intending to machine those 2 grooves with that same tool since it does not fit. But, Fusion is not clever enough to see that, and it generates a path for those depths.
Now if you turn this option off, it won't cut anything, because the bottom height is set to the model bottom, and at model bottom there is no flat face to machine. So you need this option ON, but with this option ON, it will generate a path on all the depths, which is why I think you are a bit screwed, you can't really automate it it seems to me. You will be forced to pick the floor as the bottom height.
I can't think of a way to make this automation possible for you. Maybe @engineguy can think of something, he's pretty handy with this kind of stuff. Anyways, to me, Fusion is lacking a bit here.