Extended versions of the residual cutting method, which is a linear iterative solver, are proposed and then applied to the method of moments (MoM) to reduce calculation time. The MoM analyzed electromagnetic fields in lossless cubic cavities on the basis of electric field integral equations. The extended versions employed the BiCGSafe method, which is a type of product-type iterative method, as an inner iterative solver, and they virtually improved the convergence property of the inner solver particularly when the linear systems were ill-conditioned. We increased the cavity side length L from approximately 1 to 37.2 wavelengths (λ) in 0.2-λ increments, and we irregularly increased L above 37.2 λ to as high as 50.8 λ. The average time reduction ratio at around L≒37.2 λ was approximately 50%. The best time reduction ratio of 11.7% was observed when L≒35.2 λ. In addition, we demonstrated that the extended versions could converge the relative residual norms to less than 10^-7 even in a strongly ill-conditioned case at L≒19.0 λ.