  The next generation of gravitational wave detectors will improve the
detection prospects for gravitational waves from core-collapse supernovae. The
complex astrophysics involved in core-collapse supernovae pose a significant
challenge to modeling such phenomena. The Supernova Model Evidence Extractor
(SMEE) attempts to capture the main features of gravitational wave signals from
core-collapse supernovae by using numerical relativity waveforms to create
approximate models. These models can then be used to perform Bayesian model
selection to determine if the targeted astrophysical feature is present in the
gravitational wave signal. In this paper, we extend SMEE's model selection
capabilities to include features in the gravitational wave signal that are
associated with g-modes and the standing accretion shock instability. For the
first time, we test SMEE's performance using simulated data for planned future
detectors, such as the Einstein Telescope, Cosmic Explorer, and LIGO Voyager.
Further to this, we show how the performance of SMEE is improved by creating
models from the spectrograms of supernova waveforms instead of their timeseries
waveforms that contain stochastic features. In third generation detector
configurations, we find that about 50% of neutrino-driven simulations were
detectable at 100 kpc, and 10% at 275 kpc. The explosion mechanism was
correctly determined for all detected signals.
