The computational cost of detailed micro-modeling of masonry structures can be minimized with rigid block analysis methods, where a variational formulation is particularly interesting as it allows for nonlinear pushover analysis. This work investigates the accuracy of this modeling method in predicting the response of rubble stone masonry walls in shear compression tests. To this end, we extend the mathematical programming problem by including cohesion, compressive strength, and tensile strength in the formulation and implement an improved pushover procedure, which guards compatibility of the displaced shape and crack patterns at the intersection of elastic and rigid contact models. Additionally, we reduce model uncertainty, introduced through sampling material properties with distributions estimated based on results from tests on mortar masonry joints and on mortar specimens, by correlating the predicted crack patterns with the observed ones. The findings show that (i) model falsification based on crack pattern is an effective method for reducing the parameter uncertainty of stone masonry walls; and that (ii) the improved pushover procedure predicts the pre- and post-peak response of stone masonry walls very well with analysis times of less than 20 minutes for 2D models where stones and mortar are modeled explicitly.