We present a method to fabricate individually addressable junctions of self-assembled monolayers (SAMs) that builds on previous studies which have shown that soft conductive polymer top contacts virtually eliminate shorts through the SAMs. We demonstrate devices with nanoscale lateral dimensions, representing an order of magnitude reduction in device area, with high yield and relatively low device-to-device variation, improving several features of previous soft contact devices. The devices are formed in pores in an inorganic dielectric layer with features defined by e-beam lithography and dry etching. We replace the aqueous PEDOT:PSS conductive polymer used in prior devices with Aedotron P, a low-viscosity, amphiphilic polymer, allowing incorporation of self-assembled monolayers with either hydrophobic or hydrophilic termination with the same junction geometry and materials. We demonstrate the adaptability of this new design by presenting transport measurements on SAMs composed of alkanethiols with methyl, thiol, carboxyl, and azide terminations. We establish that the observed room-temperature tunnel barrier is primarily a function of monolayer thickness, independent of the terminal group's hydrophilicity. Finally, we investigate the temperature dependence of transport and show that the low-temperature behavior is based on the energy distribution of sites from which carriers can tunnel between the polymer and gold contacts, as described by a model of variable-range hopping transport in a disordered conductor.