In graphene nanoribbons (GNRs), the lateral confinement of charge carriers opens a band gap, the key feature that enables novel graphene-based electronics. Despite great progress, reliable and reproducible fabrication of single-ribbon field-effect transistors (FETs) is still a challenge, impeding the understanding of the charge transport. Here, we present reproducible fabrication of armchair GNR-FETs based on networks of nanoribbons and analyze the charge transport mechanism using nine-atom wide and, in particular, five-atom-wide GNRs with large conductivity. We show formation of reliable Ohmic contacts and a yield of functional FETs close to unity by lamination of GNRs to electrodes. Modeling the charge transport in the networks reveals that transport is governed by inter-ribbon hopping mediated by nuclear tunneling, with a hopping length comparable to the physical GNR length. Overcoming the challenge of low-yield single-ribbon transistors by the networks and identifying the corresponding charge transport mechanism is a key step forward for functionalization of GNRs.