Miura-ori tessellations, known for their simplicity and single degree of freedom, can be ingeniously reshaped by strategically introducing cuts along and across the crease pattern edges to introduce extra degrees of freedom. This article explores the design and manufacturing aspects of cut-and-fold tessellated solids of revolution, emphasizing their ability to maintain reasonable stiffness and cushioning properties. The primary focus is on creating tessellations suitable for large-scale industrial production and packaging design applications. A family of Miura-ori kirigami derivatives are explored primarily through paper models with some supporting mechanical simulations to illustrate the compliance gained by introducing cuts to the underlying crease pattern. Our interdisciplinary approach integrates quantitative analysis through mechanical simulations, providing new understanding of the structural and functional characteristics of the proposed tessellations. By optimising the cut-and-fold process, we aim to enhance the adaptability of Miura-ori structures for practical use in industries requiring robust packaging solutions. This work contributes to the advancement of tessellation design methodologies and demonstrates the potential for transformative applications in the field of industrial packaging.