We present a new method for modelling the kinematics of galaxies from interferometric observations by performing the optimization of the kinematic model parameters directly in visibility-space instead of the conventional approach of fitting velocity fields produced with the clean algorithm in real-space. We demonstrate our method on ALMA observations of 12CO (2−1), (3−2) or (4−3) emission lines from an initial sample of 30 massive 850 $\mu$m-selected dusty star-forming galaxies with far-infrared luminosities ≳ 1012 L⊙ in the redshift range z ∼ 1.2–4.7. Using the results from our modelling analysis for the 12 of the 20 sources with the highest signal-to-noise emission lines that show disk-like kinematics, we conclude the following: (i) Our sample prefers a CO-to-H2 conversion factor, of αCO = 0.74 ± 0.37; (ii) These far-infrared luminous galaxies follow a similar Tully–Fisher relation between the circular velocity, Vcirc, and baryonic mass, Mb, as less strongly star-forming samples at high redshift, but extend this relation to much higher masses – showing that these are some of the most massive disk-like galaxies in the Universe; (iii) Finally, we demonstrate support for an evolutionary link between massive high-redshift dusty star-forming galaxies and the formation of local early-type galaxies using the both the distributions of the baryonic and kinematic masses of these two populations on the Mb – σ plane and their relative space densities.