The state stocks over 500,000 trout in rivers to the east. The Vermilion is the closest. Additionally, Michigan stocks trout in a river to the north (Huron). The Ohio fish head to the lake in the spring and spend the summer in deep water to the north and east. Once they head back to the rivers in the fall, most would probably return further east than where they were stocked in the case of the far western rivers (like the Maumee). Therefore, putting fish in the Maumee would just stock more adults in rivers to the east.
The Sandusky is better suited for steelhead runs, especially when they remove the dam. It has the same issue as the Maumee - losing some of the originally stocked fish to streams to the east. I don't think the stocked Ohio fish have the great homing instinct as naturally hatched trout, so even though they may search for their original breeding grounds, they often end up in the first river that they find. Many of the Maumee fish are probably strays from the Huron (MI).