That said - re: the measurement of a volume within a gravity well - how would you measure said volume? If you were to use light, surely it would take more time from an external reference frame to traverse (external chronometer) than it would within (internal chronometer), ergo meaning that the space is equivalently larger to the decrease in the time vector (as you can only convert space into time and vice versa).
Re: voids - I know that their hypothesis is that there's more space in the voids - but why could it not equally be the fact that there is less? More time (due to very low mas density/near-absence of gravity), ergo less space - and therefore redshift due to photons decelerating relative to our frame of reference (but constant v of c in theirs) as they move back into "normal" space.
Re: spacetime "keeping time" - true - but that also depends on your premises :) I like loop quantum gravity, and view time as an entropic thermodynamic process which can't exist without interactions... although the lack of quantisation jitter seen from pulsar light suggests that this might be wrong.