Injecting signal by a transformer is a way to go.
You need to be measuring supply rail AC magnitude
and output AC magnitude at once. Then impedance
of the xfmr is a "don't-care" because you know the
two quantities for the calculation.
Now, at some point you will leave small signal domain
where PSRR is the classical linear (log) expression and
get into large signal phenomena. You might want to
start from a known "small" signal point and run up the
amplitude to whatever the dictated stimulus amplitude
may be, looking for inflection points.