  Earth-sized exoplanets that transit nearby, late spectral type red dwarfs
will be prime targets for atmospheric characterization in the coming decade.
Such systems, however, are difficult to find via wide-field transit surveys
like Kepler or TESS. Consequently, the presence of such transiting planets is
unexplored and the occurrence rates of short-period Earth-sized planets around
late M dwarfs remain poorly constrained. Here, we present the deepest
photometric monitoring campaign of 22 nearby late M dwarf stars, using data
from over 500 nights on seven 1-2 meter class telescopes. Our survey includes
all known single quiescent northern late M dwarfs within 15 pc. We use
transit-injection-and-recovery tests to quantify the completeness of our
survey, successfully identify most ($>80\%$) transiting short-period (0.5-1 d)
super-Earths ($R > 1.9 R_\oplus$), and are sensitive ($\sim50\%$) to transiting
Earth-sized planets ($1.0-1.2 R_\oplus$). Our high sensitivity to transits with
a near-zero false positive rate demonstrates an efficient survey strategy. Our
survey does not yield a transiting planet detection, yet it provides the most
sensitive upper limits on transiting planets orbiting our target stars.
Finally, we explore multiple hypotheses about the occurrence rates of
short-period planets (from Earth-sized planets to giant planets) around late M
dwarfs. We show, for example, that giant planets at short periods ($<1$ day)
are uncommon around our target stars. Our dataset provides some insight into
occurrence rates of short-period planets around TRAPPIST-1-like stars, and our
results can help test planetary formation and system evolution models, as well
as guide future observations of nearby late M dwarfs.
