The problem of numerically simulating a rapidly rotating, strong field dynamically consistent MHD dynamo is considered, and the advantages of using the magnetostrophic approximation in lieu of the momentum equation are discussed strictly in terms of lengthening the allowable time step for a given numerical method. One possible magnetostrophic state, the Taylor state, is investigated, and both the Taylor constraint and the Taylor algorithm are extended to include a family of volumes of revolution not previously studied. The Taylor algorithm is here found to be stable in the sense that it gives a good approximation to a solution of the full system as long as the equation governing the geostrophic velocity is well-posed. Conditions under which this equation becomes ill-posed and the Taylor state ends are discussed.