The metric in a gravity well like Earth's is not the Minkowski metric, so you can't interpret gravitational time dilation (which is what you are referring to by "less time" in a gravity well) the same way you would interpret time dilation in special relativity. The simplest way to see this is to observe that gravitational time dilation is present even when everything is at rest relative to each other, whereas time dilation in special relativity requires relative motion.

the "volume" of "space" measured from within Earth's gravity well out to a fixed distance (say EML-1, for the sake of argument), differs to the same volume as measured from outside of the gravity well.

This is not correct as you state it. What is correct is that the volume you measure depends on your state of motion: the volume of space you will measure out to a certain radius from the Earth will be larger if you are at rest relative to the Earth than if you are free-falling inward towards the Earth. But two observers both in the same state of motion will measure the same volume of space out to a fixed radius from the Earth, regardless of their location relative to Earth's gravity well.

If cosmic voids have less space in them

This isn't consistent with their hypothesis; their hypothesis is that the voids have more space in them, not less. So you can't combine this with anything in their model to get a valid answer; you're starting with inconsistent premises.

(i.e. more time)

Less space does not mean more time; see above.

(if you don't have any matter-energy in a volume, then what "keeps" time?)

The voids don't have zero matter-energy; they just have a lot less than other parts of the universe (at least, according to our best current observations.) That said, spacetime itself can "keep time" even if there is no matter-energy present in a particular location.

> Lavinto and co say that when light enters a Tardis region, it is deflected sharply by the greater curvature there. That’s not what astronomers observe at all

Given that "light" is, I believe, our only way to observe the universe, how can one tell that it is not deflected?

I mean if for instance the heliosphere had some unknown refractive properties, how could we discover it since we only have light to determine the position of objects outside of the solar system?

We can't easily detect small amounts of deflection in distant parts of the universe because, as you say, we usually have nothing to compare our observations to. (In the case of light being deflected by the Sun's gravity, we can compare how a certain part of the sky looks--i.e., a certain particular grouping of stars--when the Sun is in that part of the sky, vs. when it isn't, and measure the deflection that way. But for light deflection in distant parts of the universe, there's no easy way to do that.)

However, the presence of large amounts of deflection would show up easily: we would frequently see multiple images of the same objects. In fact we only see such multiple images rarely, which indicates that there aren't any regions of large light deflection in our universe.

if for instance the heliosphere had some unknown refractive properties, how could we discover it

The same way we discovered that the Sun's gravity bends light. See above.

That will only tell us about redshift/blueshift; it won't tell us anything about what path the light took to get to us.

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.

Make a lot of local measurements of small volumes, and add them up. (Yes, I know we can't actually do that with voids a billion light years away; but when the Tardis paper talks about "volume", as I read their math, that kind of measurement is what they mean.)

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)

This is true, but I do not think it means what you think it means. See below.

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)

This doesn't make sense to me. Can you give a reference or show some actual math?

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?

I didn't say there couldn't be less; I said that assuming that there was less would be inconsistent with their hypothesis (which is that there is more), so it makes no sense to combine that assumption with their hypothesis and expect a sensible answer.

that also depends on your premises

The "Tardis" paper assumes the same premises, so it seems reasonable to keep them when discussing the paper.