Ganymede's neutral and plasma environments are poorly constrained by observations. Carnielli et al. (2019) developed the first 3D ionospheric model aimed at understanding the dynamics of the present ion species and at quantifying the presence of each component in the moon's magnetosphere. The model outputs were compared with Galileo measurements of the ion energy flux, ion bulk velocity and electron number density made during the G2 flyby. A good agreement was found in terms of ion energy distribution and bulk velocity, but not in terms of electron number density. In this work, we present some improvements to our model Carnielli et al. (2019) and quantitatively address the possible sources of the discrepancy found in the electron number density between the Galileo observations and our ionospheric model. We have improved the ion model by developing a collision scheme to simulate the charge-exchange interaction between the exosphere and the ionosphere. We have simulated the energetic component of the O$_2$ population, which is missing in the exospheric model of Leblanc et al. (2017) and added it to the original distribution, hence improving its description at high altitudes. These improvements are found to be insufficient to explain the discrepancy in the electron number density. We provide arguments that the input O$_2$ exosphere is underestimated and that the plasma production acts asymmetrically between the Jovian and anti-Jovian hemispheres. In particular, we estimate that the O$_2$ column density should be greater than $10^{15}$~cm$^{-2}$, i.e., higher than previously derived upper limits (and a factor 10 higher than the values from Leblanc et al. (2017)), and that the ionization frequency from electron impact must be higher in the anti-Jovian hemisphere for the G2 flyby conditions.