  In a previous paper, we demonstrated a single-rung method for measuring
cosmological distances in active galactic nuclei (AGN) that can be used from
low redshift (z < 0.1) to high redshift (z > 3). This method relies on the
assumption that the variability seen in AGN is constrained by the speed of
light during a flare event and can therefore be used to estimate the size of an
emitting region. A limitation of this method is that previously, the Doppler
factor was required to be known. In this paper, we derive an extension of the
`standard speed-gun' method for measuring cosmological distances that depends
on the maximum intrinsic brightness temperature that a source can reach, rather
than the Doppler factor. If the precise value of the intrinsic brightness
temperature does not evolve with redshift and flares are statistically
independent, we can in principle improve the errors in measurements of the
matter content of the universe (in a flat LambdaCDM model) statistically. We
then explored how well a future observing program would constrain cosmological
parameters. We found that recovering the input cosmology depends critically on
the uncertainty of the intrinsic brightness temperature and the number of
flares observed.
