Here are all reads of Conex parameters by Auger Offline.
Likely, at least for offline, all other parameters can be populated with 0s.

const int particleID = simShower.GetPrimaryParticle();

const double Xfirst = simShower.GetXFirst();

Xmax = simShower.GetGHParameters().GetXMax();

CoordinateSystemPtr showerCS = simShower.GetShowerCoordinateSystem();

const double zenith = (-simShower.GetDirection()).GetTheta(localCS);

const double cosTheta = (-simShower.GetDirection()).GetCosTheta(localCS);

const TabulatedFunction& energyDep = simShower.GetdEdX();

const TabulatedFunction& chargeProfile = simShower.GetLongitudinalProfile();

cherenkovProfile = &simShower.GetLongitudinalProfile(ShowerSimData::eCherenkov);

int iFirstValidBin_Ne = 0;
int iLastValidBin_Ne = chargeProfile.GetNPoints() - 1;

const double eCut = simShower.GetEnergyCutoff(evt::ShowerSimData::eElectron);

Can not upload a conex example file, but here is a list of the leafs in the conex shower and header root trees. Sonja and will write a simple uproot implementation of a conex root tree writer.