One thing that helps me visualize this whenever I'm that kind of situation, is to turn on all the icons for modifier visualization on the mesh:
That way I can see each step of the array how things are going to connect and shape up in both bottom and upper parts, and I can use it to guide me, instead of having to picture it in my head.
Hmmm... ok a curve within a curve but....
The curve deforms the tread so how to know the shape to model flat so that when curved the shape is correct?
First attempt was to establish the curve and then just cut into that but I failed as I expected
I will have another go using your approach
