He must and will prove the doctor wrong. Most of us had swallowing issues. If he can find a way to swallow and then do that as much as possible, perhaps something soft and easy be it mashed potatoes with butter or ice cream or scrambled eggs, something that works. Exercise those muscles and the mechanism all he can.
This is going to take time, months not weeks and years before things level out. Courage!

@7881188 Hi. I was on a feeding tube after radiation treatment for months. Also, two Swallow Studies were done. The first one showed what your husbands result showed. The epiglottis wasn't functioning properly. I kept up with the exercises and waving the red-light therapy wand around the back of my throat. Also, I kept eating and drinking against their wishes. By the time the second study time rolled around, the flap (epiglottis) was functioning again almost normally. The feeding tube fell out on its own and that was that. It is still hard to swallow some foods and I must drink water when eating to swallow. All I can say is my situation. As long as he can cough, the little he would aspirate shouldn't hurt him. All in all, the entire healing process time it took to regain my ability to eat, and talk took one year. Patience is key here. If he gives up, he will be on a feeding tube the rest of his life. Keep up the exercises, research the red-light wand, be stubborn, and pray. Best wishes to you both.