  We present stellar specific angular momentum $j_*$ measurements of two $z\sim
1.5$ galaxies in the KGES sample and 12 DYNAMO $z\sim 0.1$ analogues of
high-redshift galaxies. We combine natural seeing integral field spectroscopic
data to trace line emission out to high multiples of effective radius $r_e$,
with adaptive optics assisted Keck/OSIRIS observations to trace the rapid rise
in rotation curve in the inner regions. Our spaxel-wise integration method
gives results that are on average within measurement uncertainty of the
traditional rotation curve model method. At $z\sim 0$, combining GMOS and
OSIRIS datasets improves the measurement uncertainty in $j_*$ from 13\% (GMOS
only) or 16\% (OSIRIS only) to 10\%. At $z\sim 1.5$, systematics allow for at
best 20\% uncertainty on $j_*$. DYNAMO analogues of high-$z$ galaxies have low
$j_*$ for their stellar mass $M_*$, and low bulge-to-total light ratio $\beta$
for their $j_*/M_*$. The high-$z$ galaxy COSMOS 127977 has $j_*/M_*$ consistent
with normal local disk galaxies, while UDS 78317 is consistent with local
analogues. However, our high-resolution OSIRIS data reveal that UDS 78317 may
be a merging system. We report a relationship between distance to the
$\beta-j_*/M_*$ plane and the ratio of velocity dispersion to rotational
velocity $\sigma/v_{max}$, where galaxies that deviate more from the plane are
more dispersion-dominated due to turbulence. Much of the scatter in $M_*-j_*$
that is not explained by variations in the bulge-to-total ratio or evolution
with redshift may be driven by increased turbulence due to star formation, or
by treating mergers as rotating disks.
