Crystal plasticity finite element (CPFE) and spectral methods are widely used to simulate and characterize the viscoplastic response of metals and alloys at microstructural scales. These direct methods remain computationally expensive for the characterization of single scale problems with complex microstructural features, and almost infeasible for multiscale analyses. The need for higher computational efficiency in this regard motivates the development of reduced order modeling (ROM) strategies. However, most of the existing reduced order modeling strategies typically require a costly construction (or training) stage to build the reduced order basis, which rely on executing simulations using the direct methods that the ROM intends to replace. In the context of reduced order eigenstrain-based homogenization method (EHM), a series of linear elastic microscale equilibrium problems need to be solved for computation of localization and interaction tensors prior to the reduced order nonlinear simulation. In the present talk, an efficient model construction strategy for the eigenstrain homogenization method (EHM) is presented using a reduced order spectral method. The approach leverages the variational spectral method in order to directly compute the localization and interaction tensors. The proposed approach leads to a stiffness matrix that scales with number of partitions rather than number of degrees of freedom in the finite element mesh. We further discuss accuracy and scalability of the method for polycrystals and increasing phase contrast. In the execution of the constructed EHM-based reduced order models, the expectation is that a trade-off exists between the order of the model (hence computational cost) and the resulting model accuracy. Model order improvement strategies typically include using more partitioning (akin to h-refinement in classical FEM) or by using non-constant reduced order basis functions (akin to p-refinement or aka, nonlinear transformation field analysis). In this study, we demonstrate the relationship between the basis function order/number and the efficiency/accuracy characteristics of the approach. The assessment is performed in the context of polycrystal plasticity microstructures.