Dear Mr Julian Barbour
Our intuition gives that Machian principle is foundation of physics, although it is not yet proved. Similar unproved intuition appears at fundamentality of consciousness and that gravitational force is different that other forces.
You wrote that time arrow is a holistic phenomenon. I wrote similarly in one old article: "Important time's arrow is also the cosmological time's arrow. It is very likely that all in our cosmos is connected, so it has the same direction of time's arrow. It is not possible to communicate with someone who travels in opposite time direction. Therefore, time's arrow at the collapse of a wave function can choose arbitrary plus or minus direction, but it is motivated by direction of time's arrow in the cosmos. (By the way, it is very likely that explanations of big-bang need improvement. For instance, why is entropy at big bang very low?! Low entropy does not happen spontaneously.) Hitoshi Kitada [15] wrote that absolute time of universe does not exist and that only time for local observers exists. This is true in principle, but time also exists as connection between local observers, local observers are connected and this gives one direction of time's arrow of cosmos."
I claim also that space-time is an emergent phenomenon caused by matter. Otherwise, interpretation of general relativity also claims, whether all matter is removed from universe, nothing remains - neither empty space. This is a holistic consequence of general relativity similarly as Machian principle is.
This is written in my essay: "SR gives also that space-time is emergent so time exists only in matter [8], although, formally, every point in space in SR has attributed time. This is rarely mentioned, but it is very important. Namely, if all matter had been removed from our universe, there would not remain anything, not even space-time. Otherwise, this is given also by GR by its "diffeomorphism invariance" and by the "background free space-time" [9, p. 138]. Similar conclusions are given also by Markopoulou, namely that space-time arises as a consequence of relations between the elementary particles (or other elements of matter) [10]."
Maybe you should mentioned in introduction that quantum field theory is also holistic principle where field is more important than single particles.
My speculation: Maybe all universe has also properties of a particle. Otherwise, I am sure that black holes are elementary particles, maybe also universe is one particle, that means that it shows some properties of elementary particles.
Because of clarity it should be mentioned that Machian principle is also generalization of relativization: relations between objects are more important than location in one inertial system or in one coordinate system - similarly is at relativity principle.
Maybe You should explicitly mentioned that because angular momentum of universe is zero and because universe is finite, the Newton's bucket is so explained as not contradictory with Machian principle.
You replace time with time of universe. This is a cunning and something grounded idea, maybe it will show as good.
You mentioned that only six components of metric tensor is physically important, this means one volume and five angles. I do not understand what means which component? Can you explain this on three and two dimensional metric tensor and on a four dimensional example of Schwarzschild Black hole. Here non-diagonal components are zero, thus angles are only 90°? Do You think also about angles between coordinate axes?
You write also about dimensionless quantities. Do you see any advantage of using Planck's distance.
I suspect in my essay, that interior of black holes does not exist, similarly as tahions do not exist. Is this in any accordance with Your theory? Do You propose and novelty about Big Bang?
Otherwise You write very clearly.