  We present a comprehensive characterization of the evolved thermally pulsing
asymptotic giant branch (TP-AGB) star R Hydrae, building on the techniques
applied in Stellar Evolution in Real Time I (Moln\'ar et al. 2019) to T Ursae
Minoris. We compute over 3000 theoretical TP-AGB pulse spectra using MESA and
GYRE and combine these with classical observational constraints and nearly 400
years of measurements of R Hya's period evolution to fit R Hya's evolutionary
and asteroseismic features. Two hypotheses for the mode driving R Hya's period
are considered. Solutions that identify this as the fundamental mode (FM) as
well as the first overtone (O1) are consistent with observations. Using a
variety of statistical tests, we find that R Hya is most likely driven by the
FM and currently occupies the ``power down'' phase of an intermediate pulse (TP
~ 9-16). We predict that its pulsation period will continue to shorten for
millennia. Using supplementary calculations from the Monash stellar evolution
code, we also find that R Hya is likely to have undergone third dredge-up in
its most recent pulse. The MESA+GYRE model grid used in this analysis includes
exact solutions to the adiabatic equations of stellar oscillation for the first
10 radial-order pressure modes for every time step in every evolutionary track.
The grid is fully open-source and packaged with a data visualization
application. This is the first publicly available grid of TP-AGB models with
seismology produced with MESA.
