> local groups (of galaxies) [have] more spacetime [...] created inside of them

No. For all practical purposes (FAPP), galaxy clusters are not expanding. Swiss cheese cosmologies where Lemaître-Tolman-Bondi (LTB) solution vacuoles are embeded within the usual Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological solution generate observables that closely match luminosity-redshift and angular diamater-redshift relations for active galactic nuclei (SN Ia supernovae) extremely well.

LTB is a contracting spacetime -- there simply is no expansion within the vacuole, mathematically. Adding in expansion gives you something other than LTB, which leads to a different redshift for AGNs and SNs in the same cluster when correcting for peculiar motion within the cluster. The evidence favours LTB, and the physical interpretation is that the galaxy clusters and the gas surrounding them are condensing into a point over cosmologically long periods, while the galaxy clusters separate according to the surrounding expanding FLRW solution (which captures the Lyman-alpha forest, and the CMB redshift, among other observables).

Moreover, at the scale of the solar system, there is simply no measurable metric expansion. FAPP the solar system matches an LTB solution.

Since LTB solutions are asymptotically flat, we can nest them hierarchically, using an Israel-Darmois thin shell junction to capture how radiation and other matter moves between the nested LTB solutions and between the "outer" LTB solution for the vacuole in general and the FLRW solution. This works reasonably well, and there have been good numerical approaches since the mid-1990s (Musgrave, 1996).

> every single object in the universe moves exactly and precisely at the speed of light through spacetime

No. In General Relativity velocity vectors are ambiguous except at a coincident point. At a point occupied by a massless particle or wave (a photon or classical light, for instance) and one occupied by a massive particle, one can clearly and unambiguously demonstrate that the former is faster.

In a Lorentzian manifold, like our universe, there is a clear distinction between lightlike and timelike geodesics; light couples to one but not the other, and anything massive couples only to timelike (and not lightlike) geodesics. This is an inevitable consequence of the 1+3 dimensional geometry: https://en.wikipedia.org/wiki/Causal_structure#Tangent_vecto...

Light (and other massless waves or particles, those with "null" mass) simply do not have access to the same tangent vectors as massive objects, and vice-versa. This is extremely well supported by experiment and observation: https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi...

> a photon is moving only through space and has no time

A classical light wave is either at a point in spacetime or it is not. Quantum mechanical photons do not much differ.

"Movement through spacetime" is because you have chosen to split up the whole spacetime into spaces oriented by time, turning a worldline/worldtube into a set of time-ordered points. But your choice of splitting is not the right splitting any more than anyone elses. I can choose to split the universe into spaces oriented along the path of a photon emitted from a distant galaxy to my CCD detector. Or from the lightbulb across the room to my eyeball. It was obviously still in the distant galaxy, or in the filament, in my idea of the past, and a bit less past it was in flight between the two (if you believe in physical realism). That is, applying our favoured splitting to a system does not change the underlying worldtube, only how we label any given part of it.

One can carve a lightlike geodesic up however you like, for example, by assigning any sort of ordered labels between the emission and absorption. Done carefully, you can use the affine parameter which has some useful properties for calculating things like redshift (details: https://physics.stackexchange.com/questions/17509/what-is-th... ).

What one cannot do is just use the same proper time as we can on timelike geodesics. That's because proper time is defined for timelike geodesics, and those cannot be occupied by light.

Moreover, we return to the point above about ambiguity. By fixing a coordinate system -- in this case the cosmological frame, which are 3d-spaces ordered by the cosmological scale factor -- we can certainly talk about "a" global clock being used to compare the speed of light waves/photons versus neutrinos or protons. Other clocks are available, there's nothing special about the cosmological frame other than being calculationally useful and recoverable in principle by all physical observers that interact with electromagnetism. The fact that we are not compelled to use the cosmological frame is a manifestation of the ambiguity. That's why we are interested in coincident points: where a particle interacts with a detector, all observers can compare the particle momentum with the detector momentum, and transform the comparisons from observer to observer.

So, "a classical light wave traces out a lightlike path between creation and annihilation" is correct, and introducing "photon" into the mix doesn't change things much (there are various definitions of photon, incidentally); "we can carve up a lightlike path using a parameter conceptually comparable to proper time"; "we cannot use proper time as labels on a null geodesic as such, but we can certainly consider the limit as we take a low-mass ultra-relativistic particle's mass to zero as a decent proxy".

Your other points -- about the metric expansion and vacuum, in particular --are matters of interpretation of the mathematical details that are fine enough at this level, although they are far from the only physical interpretations available.