Don't give up hope. He should be right at the turning point where it will suddenly stop being such a major problem. There are different meds that can be taken to mitigate the mucous but be aware that some can temporarily make drymouth worse. Thrush can also be a contributor at his early srtage of post Tx.

Things that sort of worked for me was insuring that my throat was as clear as possible before eating anything. Water, carbonated water and different swish and spit solutions such as saline, baking soda, etc. may help. Start with the least toxic and experiment with different things. Sleep slightly elevated as well. I also ran (and still do) a humidifier 24/7. See if the doctor has any suggestions as well.