I wonder whether anyone exactly knows the mechanism:)

There are several models of charge transport and charge transfer and you may try to fit these models to your experimental findings. The first is to establish the charge carriers: electronic or ionic. If pressure dependent conductivity data are available, you may decide: in principe ionic conduction decreases, eletronic one increases with pressure. The next is to decide the sign of the charge carrier. If the mobility and the conductivity are high enough you may decide the sign of the majority charge carrier by the Hall effect measurement. Of course, it frequently happens that you have a combination of instinsic conduction and impurity conduction. In polyconjugated conducting polymers the intrinsic conduction is mostly electronic, the impurity conduction may be ionic or electronic. (Electronic may mean hole conduction as well). Usually within the conjugated molecule the band representation (with localized states) can be more or less used. Between the molecules, between the molecule and the electrode and between the molecule and a metal particle (be it nanoparticle or microparticle) the charges can be transferred by thermally hopping, by tunneling or by other mechanisms. There is no easy way of description, maybe only in nearly ideal systems. The only thing you can do is to review the models and try to fit the I-V curves, the temperature, frequency and pressure dependeces of the observed currents with the model. Aftrewards you still may only say the the measurements do not contradict this or that model. The situation is further complicted by noise and the by the finite quality of the fitting procedure. You may get acceptable fits to more than one model. The question is whether you are theoretically or exprimentally inclided person, or maybe an engineer. if you are theretically oriented, you will try to move towards better defined, idealistic systems. If you are experimentally oriented, you will try to attack the probelm by as many methods as possible and try to eliminate inconsitent theories. If you ar engineer you will be content with empirical fit and will strive to make the results reporducible and will try to use it for practical applications. (By the way the title of the discussion is different from the question you raised in the description of the topic. I reflected to the second one).

Since, its a heterogeneous system of metal/polymer composites, you can explain variation in conductivity with metal concentration by 'percolation theory' . Depending on the shape & size of the metal particles, you can fit semi-empirical models. Read this book "Hopping Conduction in Solids" by H.Bottger and V.V.Bryskin.

Regarding dispersion, it depends on the type of metal, size, shape, type of polymer..... solvent dispersion with surfactants can be a good start.