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The chain of measurements is like this starting from the size of the earth's orbit which can be measured very accurately using parallax and radar based measurements. The distance to local stars can be measured geometrically using parallax caused by the earth's orbit. This allows the main sequence of stellar temperatures and brightness to be confirmed it also allows the period luminosity levels of a few cephied variables (stars that oscillate at a particular frequency determined by their size and mass) to be measured directly and matched to the much larger numbers in globular clusters. This gives several independent distance tools which are used to measure the distances to many stars in reasonably nearby galaxies nowadays this involves very many galaxies out as far as the big virgo cluster. At this distance red shift effects are just about detectable but need a lot of statistics to separate them from the the independent motions of the galaxies themselves as they orbit the centre of the cluster. Beyond this detailed structures of galaxies globular clusters and the very brightest stars allow distances to galaxies to be estimated independently of the red shift data. Beyond this its almost all red shifts until you get type 1a supernovae. There is always activity to add new yardsticks to this basic distance scale because it would be nice to know if the red shift pattern had any small variations in it due to broad structural features For example does it depend slightly on the density of dark matter or ordinary matter. This could be an indication of other properties of dark matter and dark energy and help the theoreticians.
As I understand it, there is very little that can be used to judge large distance and the Hubble red-shift is the primary tool. What bothers me is the red shift could have more than one cause and this isn't being taken into account when estimating distance. If the passage of time was slower in the past and is speeding up, this would look the same as an expanding universe. A large survey of type 1A supernova seemed to indicate that the passage of time could have been slower in the past as the brightness did not match the red-shift.