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The kinetic Sunyaev-Zel'dovich (kSZ) effect is a secondary cosmic microwave background (CMB) anisotropy induced by the scattering of CMB photons off intervening electrons. Through cross-correlations with tracers of large-scale structure, the kSZ effect can be used to reconstruct the 3-dimensional radial-velocity field, a technique known as kSZ tomography. We explore the cross-correlation between the CMB and line-intensity fluctuations to retrieve the late-time kSZ signal across a wide redshift range. We focus on the CII emission line, and predict the signal-to-noise ratio of the kSZ tomography signal between redshifts $z=1-5$ for upcoming experiments. We show that while instruments currently under construction may reach a low-significance detection of kSZ tomography, next-generation experiments will achieve greater sensitivity, with a detection significance of $\mathcal{O}(10^2-10^3)$. Due to sample-variance cancellation, the cross-correlation between the reconstructed velocity field from kSZ tomography and intensity fluctuations can improve measurements of %the scale-dependent bias contributions from new physics to the power spectrum at large scales. To illustrate this improvement, we consider models of the early Universe that induce primordial local-type non-gaussianity and correlated compensated isocurvature perturbations. We show that with CMB-S4 and an AtLAST-like survey, the uncertainty on $f_{\rm NL}$ and $A_{\rm CIP}$ can be reduced by a factor of $\sim 3$, achieving $σ(f_{\rm NL}) \lesssim 1$. We further show that probing both low and high redshifts is crucial to break the degeneracy between the two parameters.