Discretization of a boundary-value problem with the eXtended Element-Free Galerkin (X-EFG) method yields an asymmetric EFG-type Saddle-Point (EFG-SP) problem that is difficult to solve numerically. As a high-performance solver for the problem, the Asymmetric-version improved Variable-Reduction Method (AiVRM) and its variant AiVRM2 were developed. However, it is not clear whether AiVRM2 is the only variant of AiVRM. In the present study, two other variants of AiVRM are formulated successfully by generalizing the derivation process of AiVRM and AiVRM2. A numerical code is developed for solving asymmetric EFG-SP problems with four types of AiVRMs and, by means of the code, performances of the four methods are investigated numerically. Consequently, it is found that, especially for large-scale asymmetric EFG-SP problems, four types of AiVRMs are even superior to preconditioned Krylov subspace methods.