  Analogue space-times (and in particular metamaterial analogue space-times)
have a long varied and complex history. Much of the previous related work has
focused on spherically symmetric models; however, axial symmetry is much more
relevant for mimicking rotating systems. It is well known that physically
reasonable stationary axisymmetric space-times can, under very mild technical
conditions, be put into Boyer--Lindquist form. Unfortunately, a metric
presented in Boyer--Lindquist form is not well adapted to the "quasi-Cartesian"
analysis that we developed in our previous articles on "bespoke analogue
space-times". Herein, we shall first focus specifically on various space-time
metrics presented in Boyer--Lindquist form, and subsequently determine a
suitable set of equivalent metamaterial susceptibility tensors in a laboratory
setting. We shall then turn to analyzing generic space-times, not even
necessarily stationary, again determining a suitable set of equivalent
metamaterial susceptibility tensors. Perhaps surprisingly, we find that the
well-known ADM formalism proves to be not particularly useful, and that instead
the dual "threaded" (Kaluza--Klein--inspired) formalism provides much more
tractable results. While the background laboratory metric is (for mathematical
simplicity and physical plausibility) always taken to be Riemann flat, we
{will} allow for arbitrary curvilinear coordinate systems on the flat
background space-time. Finally, for completeness, we shall reconsider
spherically symmetric space-times, but now in general spherical polar
coordinates rather than quasi-Cartesian coordinates. In summary, this article
provides a set of general-purpose calculational tools that can readily be
adapted for mimicking various interesting (curved) space-times by using
nontrivial susceptibility tensors in general (background-flat) laboratory
settings.
