The nearly all-sky TESS Full Frame Images have led to an explosion of new exoplanet discoveries. However, transit searches rely on automated pipelines to detect planets, and some planets are being missed. In particular, planets orbiting subgiant and red giant branch stars exhibit noisier and longer duration transits than similar planets around main sequence stars due to the increased radii of their host stars. Additionally, these low signal-to-noise transits can last longer than 6 hours, and have been diluted or missed entirely by other planet transit searches using TESS data. We present new planet discoveries using a novel transit search pipeline optimized for giant stars, including the confirmation of four published planets and dozens of new candidates. With the inclusion of transit detections unique to our pipeline, we determine preliminary occurrence rates of planets orbiting evolved stars and shed light on the mysteries of planetary system evolution, in particular the timescales and rates of planetary atmosphere inflation, orbital decay and inspiral, and eventual engulfment.