Planets residing in circumstellar habitable zones offer us the best opportunities to test hypotheses of life's potential pervasiveness and complexity. Constraining the precise boundaries of habitability and its observational discriminants is critical to maximizing our chances at remote life detection with future instruments. Conventionally, calculations of the inner edge of the habitable zone (IHZ) have been performed using both 1D radiative-convective and 3D general circulation models. However, these models lack interactive 3D chemistry and do not resolve the mesosphere and lower thermosphere region of the upper atmosphere. Here, we employ a 3D high-top chemistry-climate model (CCM) to simulate the atmospheres of synchronously rotating planets orbiting at the inner edge of habitable zones of K- and M-dwarf stars (between Teff = 2600 and 4000 K). While our IHZ climate predictions are in good agreement with general circulation model studies, we find noteworthy departures in simulated ozone and HOx photochemistry. For instance, climates around inactive stars do not typically enter the classical moist greenhouse regime even with high ( 10−3 mol mol−1) stratospheric water vapor mixing ratios, which suggests that planets around inactive M-stars may only experience minor water-loss over geologically significant timescales. In addition, we find much thinner ozone layers on potentially habitable moist greenhouse atmospheres, as ozone experiences rapid destruction via reaction with hydrogen oxide radicals. Using our CCM results as inputs, our simulated transmission spectra show that both water vapor and ozone features could be detectable by instruments NIRSpec and MIRI LRS on board the James Webb Space Telescope.