classical mechanics - How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?

I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance.

Here is the same list, minus Machian Space-time, with good descriptions of what symmetries they have or world line structures they possess as inertial.

Machian comes straight after leibnizian with the only invariant being relative particle distances. Its structures including only absolute simultaneity and an structure on instantaneous spaces.

Symmetries (Machian):

For comparison, here are the symmetries for Neo-Newtonian space-time:

& its cousin Full Newtonian space-time:

. . . right from World Enough and Space-Time.

Aristotelian, Full-newtonian, and Neo-newtonian are very self explanatory and the #2 & #3 of these is closest to our everyday experiences as well as being introduced to us at an early age as a grounding for classical physics.

But how would a Maxwellian, Leibinzian, or Machian universe appear to any observer in it. Heck, it is already pretty mind-blowing trying to imagine acceleration as not absolute but relative. How would this work out. . . what would transformations in this space look like mathematically? Do these contain too little structure in their space-times to even be comparable to a galilean or full newtonian space-time? Are these too alien to us?