Nice solution, Henry. There's another way. A tapered fillet on a prism will also unfold, and in a production scenario has only one neck curve to cut.
*edit* I thought about this a couple minutes after I posted and realised that the way I'd described it, the blend profile would be normal to the slope of the shoulder, and that the profile at the top of the shape would be four elliptical arcs, rather than a circle. So, back to first principles. Why won't TC unwrap the loft? For perfect sheet development, you need a ruled surface comprised of triangular faces only. An exploded TC loft of this shape gives quadrilaterals. Moreover, they overlap. Exploding a loft with line guides down the shoulders left quads that span both profiles, which should be more likely to unwrap, but still no result. A bit more thought later, I realised that the answer is with the offset cone tool.
Check the 2D profile box, and the offset cone box. Use a 90 degree arc segment for the base instead of the circular profile. Resultant open offset cone surface will unwrap, and is one curved cut and uninterrupted creases.
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