Dick,
There is one other reason for the iceberg that you described, and that is inadequate ventilation in the cabinet around the U-Line, especially in hot weather. The cooling for the interior of the unit is all located around the tray assembly, and with the hot compressor located just behind the rear of the unit, it can cause a thawing and refreezing in the rear of the bucket. If your icemaker was not producing ice adequately, I would suspect it's fan that cool the coils below it, but since ice production is good, if cube reduction does not work, I would install a muffin fan to ventilate the cabinet enclosure are the unit.
Gerald