A methodology based on configuration-state-function generators (CSFGs) has recently been implemented in the General-Purpose Relativistic Atomic Structure Package (grasp) to reduce the computational load of configuration-interaction (CI) calculations Y. T. Li et al., Comput. Phys. Commun. 283, 108562 (2023)10.1016/j.cpc.2022.108562. Large CI calculations can be performed if part of the interaction is treated perturbatively. Here, we present enhancements to the perturbative estimates by implementing blockwise methods, where the blocks are given by configuration-state-functions spanned by CSFGs. We compute excitation energies for 4s24p64d, 4s24p64f, and 4s24p54d2 states in Rb-like W37+ and corresponding transition wavelengths and rates to evaluate the methods. The final relative difference between calculated and experimental wavelengths is 0.01%. Thus, the calculations provide highly accurate values for W37+ properties useful for a variety of applications, including fusion applications.