We present Data Release 6 of ThrUMMS, consisting of complete data cubes and various moments of line emission ($^{12}$CO, $^{13}$CO, C$^{18}$O) from molecular clouds, across 60$^{\circ}$$\times$2$^{\circ}$ of the Fourth Quadrant (4Q) of the Milky Way at a resolution of 72$''$ in (l,b) and 0.09 kms$^{-1}$ in V$_{LSR}$. From LTE radiative transfer analysis of the data cubes, we compute cubes and moments of the lines' opacity, excitation temperature, and column density $N_{12CO}$. Combining $I_{12CO}$ and $N_{12CO}$ data, we derive a global mass conversion law $N$=$N_{0}I^{p}$, where $N_{0}$$\approx$10$^{18}$mol/m$^{2}$ and $p$=2 at this resolution. We argue that the standard linear $N$=$XI$ is only approximately valid: $p$$\sim$1.5-1.0 at coarser resolutions or in atypical locations, such as Galactic Center clouds. Also, the velocity dispersion distributions are very different between $I_{12CO}$ and $N_{12CO}$, the former preferentially tracing more diffuse molecular gas. We re-evaluated Galactic rotation parameters for the 4Q, defining a new ``BGT'' model, and deprojected the (l,V) data onto (l,d) and (x,y) grids using standard kinematic procedures. To automate distance disambiguation inside the solar circle, we developed a simple $\zeta^{+}$ discriminator function and applied it to our deprojections. We discovered two previously unrecognised features of the molecular cloud population: widespread ripples in the midplane of wavelength 4kpc and amplitude 50pc, potentially generated by the last perigalactic passage of the Sgr dwarf; and three distant, massive molecular structures, the Far Ara clouds, two of which exhibit an exceptional velocity gradient, possibly arising in a massive spiral feather or a gas-rich dwarf galaxy $\sim$20--300kpc beyond the disk.
Comment: Submitted to AAS Journals; comments welcome! Main paper 15 pages, 10 figures. Appendix A 15 pages, 11 figures. Appendix B 11 pages, 10 figures. Appendix C 45 pages, 36 figures