I'd fill it again and put a piece of cardboard under it or a clean rag. See where it is leaking out. Seems impossible to me that it's actually leaking out while it's sitting (and not running.)
My money is on your transmission cooler. They are designed so that the tranmission oil pressure is higher than the water pressure. This means that the tranny fluid is supposed to leak out before the water can leak in. Easy to pull it off and pressure test it.
Former owner of a 1987 Supra Saltare. Current owner of a Malibu 23LSV.