I think you have made a very interesting study, and clearly shown how the gate voltage actually tunes the electron charge in the central region, by adding and removing charge. Sure, a positive value would mean charge is moved from the electrode to the central region (the part you use to sum up the charge), which is allowed since the system is in non-equillibrium and we have non-conservation of charge.
To relate the conductance to the charge, you probably have to analyze the transmission spectrum, and perhaps also the molecular levels, and see how these change with the gate. They probably move, and that's why the conductance changes. Depending on the nature of these levels, etc, you can analyze the system further. There is no simple way to say whether adding or removing electrons will decrease or increase the current/conductance, it depends on the details, but basically this is the working principle of a transistor, where the primary current (source drain) is controlled by a much smaller current (the gate).
Based on this, and other things too perhaps, you can hopefully draw your conclusions and publish a nice paper
You may want to have a look at how other people analyze systems with a gate voltage, and compute various quantities. Search for "transistor" on
the publication page and see e.g. the two graphene articles from 2007.
