Well. if you remove time you also remove the dynamics of a universe, as it seems to me? It becomes easier to handle as you get one 'flat static slice of SpaceTime'. But you also get only one description. To me the idea behind relativity is lights speed in a vacuum, and as far as I'm concerned that must hold in both SR and GR, for those that split it.

That constant in a dynamic universe, defined by and through change, gives each observer different 'dynamic 3D slices' described through times arrow. To each observer that arrow is the same as I see it, and the proof for that is simple, you just need to superimpose them to see that all clocks have a same rate of change, using radiation. So everyones arrow must become a local definition which also must be true, as far as I can see.

That a Lorentz transformation always will give you your conceptual SpaceTime is easily explained through radiations constant, and is something of a misnomer to me as it to many seems as a proof of one whole united indivisible SpaceTime, same for all. To me that 'truth' is more subtle, what makes a Lorenz transformation possible is lights speed in a vacuum. And the only thing such a transformation state is the same as Einstein once went out from. That light is a constant.

To lift out 'the arrow' you, I don't know? A quantum computer comes to mind, or better still, indeterminacy. 'Virtual photons' do not fit such a concept though, as the idea behind it, to me, is something 'existing in time', at least as I think of it.