I find that most of my secretions originate just above the cuff. If the cuff is not fully inflated, gravity causes the secretions to run down into my lungs. This could be the reason your Dad's lungs are so full.
It is also important to keep up with trach suctioning. If secretions are too thick for the suction machine, he may need more water. If water doesn't help, a Cough Assist Machine always does the trick.