Conductance is the derivative of the current with respect to the bias voltage applied, i.e., G = dI/dV. It means that even when the current is zero, e.g., at V=0, conductance has a finite value. So, I do not understand your concern regarding low current vs. high conductance - it is like comparing apples with oranges. Small values for a given quantity do not mean immediately that the derivative values of that quantity are small.
Regarding calculating the current from the transmission spectrum obtained at zero-bias voltage, 0 V. You can do it indeed - this is called linear response approximation. It is valid for some systems voltage ranges, but it may fail for the others. In the latter case, you have to calculate the current in a self-consistent manner for each bias point. Whether linear response approximation holds for your system of study, I do not know, and that is something you should investigate.