Rubber components are widely spread in engineering due to their mechanical properties such as high strength, elongation, and dissipation characteristics. Modeling rubber behavior poses challenges because of its complex visco-elastic properties and various nonlinear effects. As high fidelity simulations become increasingly challenging, reduction techniques such as subspace projection and hyper-reduction have emerged, which seek to achieve efficient use of complex models while reducing computational demands.This article presents a Python-Abaqus co-simulation framework to perform the Energy Conserving Sampling and Weighting (ECSW) hyperreduction on nonlinear finite element hyper-viscoelastic models. A novel approach based on incremental elementary work is formulated to optimize the element selection in ECSW in the attempt of exploiting the rate dependent material characteristics. The successful implementation of the co-simulation framework underscores the beneficial use of commercial code capabilities in the development of nonlinear reduction algorithms. A numerical cantilever beam subjected to dynamic loading is employed to explore the potential of the newly proposed ECSW variant.