We describe a project to develop new medium-energy gamma-ray instrumentation by constructing and flying a balloon-borne Compton telescope using advanced scintillator materials combined with silicon photomultiplier readouts. There is a need in high-energy astronomy for a medium-energy gamma-ray mission covering the energy range from approximately 0.4 - 20 MeV to follow the success of the COMPTEL instrument on CGRO. We believe that directly building on the legacy of COMPTEL, using relatively robust, low-cost, off-the-shelf technologies, is the most promising path for such a mission. Fortunately, high-performance scintillators, such as Lanthanum Bromide (LaBr3), Cerium Bromide (CeBr3), and p-terphenyl, and compact readout devices, such as silicon photomultipliers (SiPMs), are already commercially available and capable of meeting this need. We have conducted two balloon flights of prototype instruments to test these technologies. The first, in 2011, demonstrated that a Compton telescope consisting of an liquid organic scintillator scattering layer and a LaBr3 calorimeter effectively rejects background under balloon-flight conditions, using time-of-flight (ToF) discrimination. The second, in 2014, showed that a telescope using an organic stilbene crystal scattering element and a LaBr3 calorimeter with SiPM readouts can achieve similar ToF performance. We are now constructing a much larger balloon instrument, an Advanced Scintillator Compton Telescope (ASCOT) with SiPM readout, with the goal of imaging the Crab Nebula at MeV energies in a one-day flight. We expect a ~4σ detection up to ~1 MeV in a single transit. We present calibration results of the first detector modules, and updated simulations of the balloon instrument sensitivity. If successful, this project will demonstrate that the energy, timing, and position resolution of this technology are sufficient to achieve an order of magnitude improvement in sensitivity in the mediumenergy gamma-ray band, were it to be applied to a ~1 cubic meter instrument on a long-duration balloon or Explorer platform.