  The EXperiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) is a
balloon-borne cryogenic telescope that will survey the spectrum of diffuse
emission from both the Milky Way and the cosmic web to probe star formation,
the interstellar medium, and galaxy evolution across cosmic time. EXCLAIM's
primary extragalactic science survey maps 305 deg$^2$ along the celestial
equator with an R=512 spectrometer over the frequency range \nu=420-540 GHz,
targeting emission of the [CII] line over redshifts 2.5<z<3.5 and several CO
lines for z<1. Cross-correlation with galaxy redshift catalogs isolates line
emission from the large-scale structure at target redshifts. In this paper, we
forecast the sensitivity for both the two-point and conditional one-point
cross-correlation. We predict that EXCLAIM will detect both the [CII]-QSO
cross-power spectrum and the conditional voxel intensity distribution (CVID) at
various redshifts under a broad range of [CII] intensity models, allowing it to
differentiate among these models in the literature. These forecasts for the
power spectra include the effects of line interlopers and continuum foreground
contamination. We then convert the joint [CII] constraints from both the
cross-power spectrum and the CVID into constraints on the [CII] halo
luminosity-mass relation $L_\mathrm{[CII]}(M)$ model parameters and the star
formation rate density (SFRD) from [CII] emission. We also develop sensitivity
estimates for CO, showing the ability to differentiate between models.
