  It has been long believed that oblique and quasi-perpendicular configurations
in supernova remnants (SNRs) were inefficient at injecting ions into diffusive
shock acceleration (DSA), and that the highest energy Galactic cosmic rays
(CRs) must come from parallel or quasi-parallel shocks. However, recent 3D
kinetic simulations have shown that high-obliquity shocks can successfully
energize particles and produce amplified magnetic fields in the upstream. We
aim to investigate the maximum energy particles it is possible to produce in
oblique and quasi-perpendicular shocks and whether they are capable of
triggering the non-resonant hybrid instability (NRHI). We present a novel setup
for hybrid simulations of non-relativistic shocks that use a "faux shock"
boundary condition instead of a real shock to significantly reduce the
computational cost and that can be run for long enough to study the late-time
behaviors of these systems. Our results show that it may be possible for
oblique and quasi-perpendicular shocks to transition from early periods of
shock drift acceleration (SDA) into DSA at later times, giving particles a
brief period of rapid acceleration followed by a long-duration, self-sustaining
period of slower energy growth. Furthermore, we find evidence that the NRHI is
triggered in the upstream at late times. Oblique and quasi-perpendicular shocks
may be an important contributor to high energy CRs, potentially even
responsible for the knee in the CR energy spectrum.
