I had the same thought about vertical wedges (like a globe or an orange slice) for the primary hull as well- but I don't think it would work.
One of the main problems working with paper/cardstock is that paper doesn't like to bend in more than one direction. The strip method used in this model actually requires only one real bend in the strip- the strip is cut in such a way as to avoid that second bend.
If you and I are thinking along the same lines, the map shapes in this video are what we're envisioning.
https://www.youtube.com/watch?v=4RWcWSN4HhI
The globe slice approach would required that the piece curve not only from top to bottom (north-to-south), but would also have to be bent from one side to the other to account for the east-to-west curvature of the Earth.
The globe makers can use that shape because 1) the paper they're using is far thinner than anything we have access to, and 2) because they have a solid surface upon which to place and shape the paper.
Using cardstock, you're not going to be able to replicate that working surface or the curvature- which means you're going to wind up with a faceted look. You could minimize the east-west bend by using narrower strips, but this means a lot more cutting, gluing, and seams. And even then, the facets will be visible when the model is examined closely.
And no.
I have no idea what those grey circles were for.
