Direct-to-Satellite-IoT (DtS-IoT) is a promising approach for data transfer to/from IoT devices in remote areas where deploying terrestrial infrastructure is not appealing or feasible. In this context, Low-Earth Orbit (LEO) satellites can serve as passing-by IoT gateways to which devices can offload buffered data to. However, transmission distance and orbital dynamics, combined with highly constrained devices on the ground makes DtS-IoT a very challenging problem. In fact, existing IoT medium access control protocols, negotiations schemes, etc. need to be revised and/or extended to scale up to these challenging conditions. The intricate time-dynamic aspects of DtS-IoT networks require of adequate simulation environments to assess the expected performance of enabling technologies. To make up for the lack of such tools, we present a novel event-driven open-source end-to-end simulation tool coined FLORASAT. The simulator leverages Omnet++ and includes a benchmarking DtS-IoT scenario comprising 16 cross-linked LEO satellites and 1500 IoT nodes on the surface. Satellites and devices are connected using the standard LoRaWAN Low-Power Wide Area (LPWAN) protocol (Class A and B). FLoRaSat allows the easy implementation and study of DtS-IoT radio access and core network protocols, and we take advantage of this flexibility to investigate expected network metrics and non-intuitive phenomena emerging from the resulting multi-gateway setup.