Number of expected CCSN detections over the survey period of the dataset as a function of the missing fraction. Left: The GSAOI/GeMS dataset. Right: The GSAOI/GeMS dataset combined with the ALTAIR/NIRI dataset from Paper I. Red line: The mean value. Shaded red areas: 1σ and 2σ confidence intervals. Poissonian upper and lower limits due to small number statistics and the cumulative effect of other error sources are combined here. Dashed black: Number of real detected CCSNe in the survey(s). We note that while the expected CCSN counts for the datasets are 9 and 25 CCSNe for GSAOI/GeMS alone, and GSAOI/GeMS combined with ALTAIR/NIRI dataset, respectively, the Monte Carlo simulations result in detecting significantly less CCSNe even at 0% missing fraction. This is caused by a combined effect of faint CCSNe, moderate extinction and long time interval until the next observation epoch within the yielded CT.