"That qualification presupposes time asymmetry ..."
No it doesn't. Every model of classical, continuous function, physics explicitly implies time symmetry (the equations work equally well forward and backward in time). This is one of the bedrock assumptions of spacetime -- I believe what you are thinking of is the asymmetry of time in the cosmological problem.
The Minkowski metric describes an isotopic spacetime in flat Euclidean space absent of matter. Special relativity agrees; the Lorentz transformation accounts for time symmetry by a fixed point that guarantees the symmetry of two events in the spacetime interval.
When special relativity is generalized, we encounter a pseudo-Riemannian metric of Lorentzian metric properties (sometimes simply called the Lorentz metric) -- this means there is no privileged coordinate frame, no fixed point by which time symmetry is guaranteed in a continuum of uniform motion. Instead, the local flat metric of Minkowski space is continuous with the globally curved Riemannian manifold -- leading to the cosmological asymmetry of time; i.e., the singularity of creation. Short of the beginning of time itself, all observer relations are nondegenerate, meaning there is objective differentation in spacetime between observer and observed, and the symmetry of those relations guarantees equal validity of each observer's measurement. No privileged frame.
"Your brief comments on 6/30 include, "Applied to physics, the Minkowski formulation is conceptually easy and operationally hard," which hit me right off the bat (being a mathophobic), because in the teaser excerpts of the translation, Minkowski immediately dives into his arsenal of math. Kindly, sir, (I want some more porridge) do share your thoughts on why he starts with the hyberbola. What is assumed, or what did I not get to begin with?"
The Minkowski diagram is a graphic device to help us visualize the difference between spacelike separated (hyperbolic) events and timelike (parabolic) events in a simplified continuum of one dimension of space and one dimension of time. When we add the complication of observers in different states of relative motion, we can comprehend visually the effects of time dilation and length contraction described by the mathematics of the Lorentz transformation.
"I think where conceptually there is resistance to 'inertial motion' along a worldline, is what seems to be contradictory with the acknowledgement by both Minkowski and Einstein that fields, or 'something(s) perceptible', exists throughout universal space//time. So What?"
Well, if "no space is empty of the field," no space is empty of observation (no nonlocality) even in spacelike separated events.
In fact, bodies do not resist their motion, as Petkov elegantly explains in this FQXi essay.
"I don't want to dance on the bar and start fights, but there would be a worldline of the magnetic equilibrium between simple macro-magnets which is experimentally interior to the domain of effect, also. And the same might be true of the neutral plane in electrical appliance. So why the hyberbola?"
Although gravitational and electromagnetic field influences are both infinite, they are not the same thing. Remember, the electromagnetic field is symmetric in time while the gravitational field operates only in the one direction -- toward the center of mass. It's the presence of matter in the universe that breaks symmetry at the singularity of creation, which is why in terms of geometry, Einstein's theory of gravity (general relativity) applies only up to diffeomorphism.