In a noisy environment with weak single levels, quantum illumination can outperform classical illumination in determining the presence and range of a target object even in the limit of sub-optimal measurements based on non-simultaneous, phase-insensitive coincidence counts. Motivated by realistic experimental protocols, we present a theoretical framework for analysing coincident multi-shot data with simple detectors. This approach allows for the often-overlooked non-coincidence data to be included, as well as providing a calibration-free threshold for inferring the presence and range of an object, enabling a fair comparison between different detection regimes. Our results quantify the advantage of quantum over classical illumination when performing target discrimination in a noisy thermal environment, including estimating the number of shots required to detect a target with a given confidence level.