In large thick plastic pipe extrusion, the residence time in the cooling chamber is long, and the melt inside the pipe sags under its own weight, causing the product to thicken on the bottom ( and to thin on the top). To compensate for sag, engineers normally shift the die centerpiece downward. This paper focuses on how this decentering triggers unintended consequences for elastic polymer melts. We employ eccentric cylindrical coordinates, to capture exactly the geometry of our problem, the flow between eccentric cylinders. Specifically, we arrive at an exact analytical expression for the axial and lateral forces on the die barrel using the polymer process partitioning approach, designed for elastic liquids. We choose the Oldroyd 8-constant framework due to its rich diversity of constitutive special cases. Since our main results are in a form of simple algebraic expression along with two sets of curves, they can thus be used not only by engineers, but any practitioner. We close our paper with detailed dimensional worked examples to help practitioners with their pipe die designs.