Understanding and controlling the electrical properties of solution-processed 2D materials is key to further printed electronics progress. Here, we demonstrate that the thermolysis of the aromatic intercalants utilized in nanosheet exfoliation for graphene laminates allows for high intrinsic mobility and the simultaneous control of doping type (n- and p-) and concentration over a wide range. We establish that the intraflake mobility is high by observing a linear magnetoresistance of such solution-processed graphene laminates and using it to devolve the interflake tunneling and intralayer magnetotransport. Consequently, we determine the temperature dependencies of the inter- and intralayer characteristics. The intraflake transport appears to be dominated by electron-phonon scattering processes at temperatures T > 20 K, while the interflake transport is governed by phonon-assisted tunneling. In particular, we identify the efficiency of phonon-assisted tunneling as the main limiting factor for electrical conductivity in graphene laminates at room temperature. We also demonstrate a thermoelectric sensitivity of around 50 μV·K-1 in a solution-processed metal-free graphene-based thermocouple.