We describe our ongoing work to develop a new medium-energy gamma-ray Compton telescope using advanced scintillator materials combined with silicon photomultiplier readouts and fly it on a scientific balloon. 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 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 are now constructing an Advanced Scintillator Compton Telescope (ASCOT) with SiPM readout, with the goal of imaging the Crab Nebula at MeV energies from a high-altitude balloon flight. We expect a ~4-sigma detection at ~1 MeV in a single transit. We present calibration results of the 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 medium-energy gamma-ray band, were it to be applied to a ~1 cubic meter instrument on a long-duration balloon or Explorer platform.