During its two-year mission at comet 67P, Rosetta nearly continuously monitored the inner coma plasma environment for gas production rates varying over three orders of magnitude, at distances to the nucleus from a few to a few hundred km. To achieve the best possible measurements, cross-calibration of the plasma instruments is needed. We construct with two different physical models to cross-calibrate the electron density as measured by the Mutual Impedance Probe (MIP) to the ion current and spacecraft potential as measured by the Rosetta Langmuir Probe (LAP), the latter validated with the Ion Composition Analyser (ICA). We retrieve a continuous plasma density dataset for the entire cometary mission with a much improved dynamical range compared to any plasma instrument alone and, at times, improve the temporal resolution from 0.24-0.74~Hz to 57.8~Hz. The new density dataset is consistent with the existing MIP density dataset and covers long time periods where densities were too low to be measured by MIP. The physical model also yields, at 3~hour time resolution, ion flow speeds as well as a proxy for the solar EUV flux from the photoemission from the Langmuir Probes. We report on two independent mission-wide estimates of the ion flow speed which are consistent with the bulk H$_2$O$^+$ ion velocities as measured by ICA. We find the ion flow to consistently be much faster than the neutral gas over the entire mission, lending further evidence that the ions are collisionally decoupled from the neutrals in the coma. RPC measurements of ion speeds are therefore not consistent with the assumptions made in previously published plasma density models of the comet ionosphere at the start and end of the mission. Also, the measured EUV flux is perfectly consistent with independently derived values previously published from Johansson et al. (2017) and lends support for the conclusions drawn therein.