Three-periodic curvilinear cylinder packings have been discussed extensively in both structural chemistry and materials science in relation to metal-organic frameworks. In some cases, the curved cylinders have a cooperative unwinding mechanism that expands the material isotropically, reminiscent of an auxetic deformation and driven purely by the geometry of the cylinders. In a previous study, such cylinder packings were modeled with a simple tensegrity, designed to represent the packing constraints of the original structure. While the framework behaved well under equilibration, its deformative behavior was rather unstable, indicating that the constraint system needs an enhanced design. Hence, we propose a new model based on the theory and physics of two filaments in tight contact that replaces a single bar at the contact of two cylinders with a tetrahedron of constraints. In combination with a homotopy continuation approach, the nonlinear constraint system leads to a robust numerical scheme for computing deformation paths. Testing this new approach in two instances of auxetic filament packings reveals the new method's significantly improved stability. Joint work with Myfanwy Evans