High-speed motions in pick-and-place operations are critical to making robots cost-effective in many automation scenarios, from warehouses and manufacturing to hospitals and homes. However, motions can be too fast -- such as when the object being transported has an open-top, is fragile, or both. One way to avoid spills or damage, is to move the arm slowly. We propose Grasp-Optimized Motion Planning for Fast Inertial Transport (GOMP-FIT), a time-optimizing motion planner based on our prior work, that includes constraints based on accelerations at the robot end-effector. With GOMP-FIT, a robot can perform high-speed motions that avoid obstacles and use inertial forces to its advantage. In experiments transporting open-top containers with varying tilt tolerances, whereas GOMP computes sub-second motions that spill up to 90% of the contents during transport, GOMP-FIT generates motions that spill 0% of contents while being slowed by as little as 0% when there are few obstacles, 30% when there are high obstacles and 45-degree tolerances, and 50% when there 15-degree tolerances and few obstacles.