I spoke too soon. This problem is still a problem same as before. The tray fills up with ice and then water spills over and lands on the floor. The back of the tray is definitely lined up with the outlet tube.
When we open the outside access to the back of the frig, we can see no drain tube/hose etc. We can see nothing that looks like some kind of drain. Short of pulling the refrigerator out of the trailer and getting behind it, we don't know what to do next. Does anyone have a good idea how we ought to proceed?