Luminescent solar concentrators (LSCs) are a promising technology to help integrate solar cells into the built environment, as they are colorful, semitransparent, and can collect diffuse light. While LSCs have traditionally been cuboidal, in recent years, a variety of unconventional geometries have arisen, for example, circular, curved, polygonal, wedged, and leaf-shaped designs. These new designs can help reduce optical losses, facilitate incorporation into the built environment, or unlock new applications. However, as fabrication of complex geometries can be time- and resource-intensive, the ability to simulate the expected LSC performance prior to production would be highly advantageous. While a variety of software exists to model LSCs, it either cannot be applied to unconventional geometries, is not open-source, or is not tractable for most users. Therefore, here we introduce a significant upgrade of the widely used Monte Carlo ray-trace software pvtrace to include: (i) the capability to characterize unconventional geometries and improved relevance to standard measurement configurations; (ii) increased computational efficiency; and (iii) a graphical user interface (GUI) for ease-of-use. We first test these new features against data from the literature as well as experimental results from in-house fabricated LSCs, with agreement within 1% obtained for the simulated versus measured external photon efficiency. We then demonstrate the broad applicability of pvtrace by simulating 20 different unconventional geometries, including a variety of different shapes and manufacturing techniques. We show that pvtrace can be used to predict the optical efficiency of 3D-printed devices. The more versatile and accessible computational workflow afforded by our new features, coupled with 3D-printed prototypes, will enable rapid screening of more intricate LSC architectures, while reducing experimental waste. Our goal is that this accelerates sustainability-driven design in the LSC field, leading to higher optical efficiency or increased utility.