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.