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The kinetic Sunyaev-Zel'dovich (kSZ) effect, i.e., the Doppler boost of cosmic microwave background (CMB) photons caused by their scattering off free electrons in galaxy clusters and groups with non-zero bulk velocity, is a powerful window on baryons in the universe. We present the first halo-model computation of the cross-power spectrum of the ``projected-field'' kSZ signal with large-scale structure (LSS) tracers. We compare and validate our calculations against previous studies, which relied on $N$-body-calibrated effective formulas rather than the halo model. We forecast results for CMB maps from the Atacama Cosmology Telescope (AdvACT), Simons Observatory (SO), and CMB-S4, and LSS survey data from the Dark Energy Survey, the Vera C.~Rubin Observatory (VRO), and \textit{Euclid}. In cross-correlation with galaxy number density, for AdvACT $\times$ \textit{unWISE} we forecast an 18$σ$ projected-field kSZ detection using data already in hand. Combining SO CMB maps and \textit{unWISE} galaxy catalogs, we expect a $62σ$ detection, yielding precise measurements of the gas density profile radial slopes. Additionally, we forecast first detections of the kSZ -- galaxy weak lensing cross-correlation with AdvACT $\times$ VRO/\textit{Euclid} (at 6$σ$) and of the kSZ -- CMB weak lensing cross-correlation with SO (at 16$σ$). Finally, $\approx 10-20$\% precision measurements of the shape of the gas density profile should be possible with CMB-S4 kSZ -- CMB lensing cross-correlation without using any external datasets.