I have a similar model, and had a similar problem. One additional symptom I had when the water was on the floor....there was a thick slab of ice on the bottom of the freezer. PROBLEM: there is a rubber funnel called a duckbill drain, on the end of the tube that drains into the pan. ( Access to that piece is through the small grill on the back, NOT through the front.) This part does not show on parts lists. Some months ago, AJ posted a whirlpool tech sheet about this item...the rubber would soften from the heat, being near the condensor coil, and clog over, preventing drain.)
If you don't have ice build up on the bottom of the freezer, then this is not your problem. But I understand it IS a fairly common problem, so I wanted to mention it.