The search for life involves assessing false positives and negatives in potentially habitable atmospheres via future missions. In paper I, we determined that ultra-violet (UV) stellar activity should not impact the detection of water vapor in moist habitable atmosphere of a synchronously rotating 1-Earth mass terrestrial aquaplanet orbiting an M dwarf host star. We also established that for an abiotic methane production rate of 108 molecules cm-2 s-1, while CH4 should be spectrally detectable for a hypothetically inactive 3300K M dwarf star, detectable CH4 is absent for realistic levels of UV activity. Abiotically sourced oxygen allotropes (O, O2, O3) and CH4 prevalent in an Earth-like planet’s atmosphere is important for gauging its habitability. However, while O2 is barely spectrally detectable in IR due to the Rayleigh scattering tail, we find that enhanced O3 from high stellar UV may be potentially detectable in the mid-infrared (MIR) with the future Origin Space Telescope. Past work has shown that O3 accumulation in these atmospheres is determined by the ratio of far-ultraviolet (FUV) to near- and mid- ultraviolet (NUV and MUV) radiation from the host star. In this paper, we robustly investigate this behavior as a function of instellation variations on the synthetic UV-active stellar fluxes from Paper I, as well as variable surface methane flux, for a range of water vapor content within the habitable zone of our 3300K star from Paper I. We employ our 1-D photochemical model from Paper I with varied stellar UV, to assess how O3 accumulation varies with CH4 production rates in these atmospheres. We find O3 accumulation in these atmospheres to be sensitive to the three factors: UV activity, the instellation level, as well as the chosen methane production rate. Temperature and H2O profiles are consistent with Paper I for our base instellation level of 1650 W/m2; we use the GCM results for lower instellation levels reported in Wolf et al. (2019). We deduce that simultaneous detection of O3 and CH4 in synchronously rotating Earth-like planets around M dwarfs may be possible for an abiotically sourced atmosphere.