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 widefield 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 m 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 days) super-Earths (R >1.9 R ⊕), and are sensitive (∼50%) to transiting Earth-sized planets (1.0-1.2 R ⊕). 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 with short periods (<1 day) are uncommon around our target stars. Our data set provides some insight into the 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.