  We consider a QCD cold plasma motivated Equation of State (EOS) to examine
the impact of an Anomalous Magnetic Moment (AMM) coupling and small shape
deformations for static oblate and prolate core shapes of quark stars. Using
the Foga\c{c}a QCD motivated EOS which shifts from the high temperature low
chemical potential quark gluon plasma environment to the low temperature high
chemical potential quark stellar core environment we consider the impact of an
AMM coupling with a metric induced shape deformation parameter in the TOV
equations. The EOS is developed using a hard gluon and soft gluon decomposition
of the gluon field tensor using a mean field effective mass for the gluons. The
AMM is considered using the Dirac spin tensor coupled to the EM field tensor
with quark flavor based magnetic moments. The shape parameter is introduced in
a metric ansatz that represents oblate and prolate static stellar cores for
modified TOV equations. These equations are numerically solved for the final
mass and radius states representing the core collapse of a massive star with a
phase transition leading to an unbound quark-gluon plasma. We find that the
combined shape parameter and AMM effects can alter the coupled EOS-TOV
equations resulting in an increase in the final mass and a decrease in the
final equatorial radius without collapsing the core into a black hole and
without violating causality constraints, we find maximum mass values in the
range: 2.3 Solar Masses < M < 2.7 Solar Masses. These states are consistent
with some astrophysical high mass magnetar/pulsar and gravity wave systems
which may provide evidence for a core that has undergone a quark-gluon phase
transition such as PSR 0943+10 and the secondary from the GW 190814 event.
