Cassini's Grand Finale orbits provided for the first time in-situ measurements of Saturn's topside ionosphere. We present the Pedersen and Hall conductivities of the top near-equatorial dayside ionosphere, derived from the in-situ measurements by the Cassini Radio and Wave Plasma Science Langmuir Probe, the Ion and Neutral Mass Spectrometer and the fluxgate magnetometer. The Pedersen and Hall conductivities are constrained to at least 10-5-10-4 S/m at (or close to) the ionospheric peak, a factor 10-100 higher than estimated previously. We show that this is due to the presence of dusty plasma in the near-equatorial ionosphere. We also show the conductive ionospheric region to be extensive, with thickness of 300-800 km. Furthermore, our results suggest a temporal variation (decrease) of the plasma densities, mean ion masses and consequently the conductivities from orbit 288 to 292.