Intensity mapping cross-correlations II: HI halo models including shot noise

H I intensity mapping data traces the large-scale structure matter distribution using the integrated emission of neutral hydrogen gas (H I). Cross-correlation of the intensity maps with optical galaxy surveys can mitigate foreground and systematic effects, but has been shown to significantly depend on galaxy evolution parameters of the H I and the optical sample. Previously, we have shown that the shot noise of the cross-correlation scales with the H I content of the optical samples, such that the shot noise estimation infers the average H I masses of these samples. In this paper, we present an adaptive framework for the cross-correlation of H I intensity maps with galaxy samples using our implementation of the halo model formalism which utilizes the halo occupation distribution of galaxies to predict their power spectra. We compare two H I population models, tracing the spatial halo and the galaxy distribution, respectively, and present their auto- and cross-power spectra with an associated galaxy sample. We find that the choice of the H I model and the distribution of the H I within the galaxy sample have little impact for the shape of the auto- and cross-correlations, but significantly affects the measured shot noise amplitude of the estimators, a finding we confirm with simulations. We demonstrate parameter estimation of the H I halo occupation models and advocate this framework for the interpretation of future experimental data, with the prospect of determining the H I masses of optical galaxy samples via the cross-correlation shot noise.