  The most stringent local measurement of the Hubble-Lema\^itre constant from
Cepheid-calibrated Type Ia supernovae (SNe~Ia) differs from the value inferred
via the cosmic microwave background radiation ({\it Planck}$+\Lambda$CDM) by
$\sim 5\sigma$. This so-called "Hubble tension" has been confirmed by other
independent methods, and thus does not appear to be a possible consequence of
systematic errors. Here, we continue upon our prior work of using Type II
supernovae to provide another, largely-independent method to measure the
Hubble-Lema\^itre constant. From 13 SNe~II with geometric, Cepheid, or tip of
the red giant branch (TRGB) host-galaxy distance measurements, we derive H$_0=
75.4^{+3.8}_{-3.7}$\,km\,s$^{-1}$\,Mpc$^{-1}$ (statistical errors only),
consistent with the local measurement but in disagreement by $\sim 2.0\sigma$
with the {\it Planck}$+\Lambda$CDM value. Using only Cepheids ($N=7$), we find
H$_0 = 77.6^{+5.2}_{-4.8}$\,km\,s$^{-1}$\,Mpc$^{-1}$, while using only TRGB
($N=5$), we derive H$_0 = 73.1^{+5.7}_{-5.3}$\,km\,s$^{-1}$\,Mpc$^{-1}$. Via 13
variants of our dataset, we derive a systematic uncertainty estimate of
1.5\,km\,s$^{-1}$\,Mpc$^{-1}$. The median value derived from these variants
differs by just 0.3\,km\,s$^{-1}$\,Mpc$^{-1}$ from that produced by our
fiducial model. Because we only replace SNe~Ia with SNe~II -- and we do not
find statistically significant difference between the Cepheid and TRGB H$_0$
measurements -- our work reveals no indication that SNe~Ia or Cepheids could be
the sources of the "H$_0$ tension." We caution, however, that our conclusions
rest upon a modest calibrator sample; as this sample grows in the future, our
results should be verified.
