I have a paralyzed left diaphragm. I treated with local doctors and then decided to go to the Mayo Clinic in Jacksonville. It was a good move.
I have heard of people suffering from a paralyzed diaphragm after surgery...from nerve damage that feeds the diaphragm. I have bilateral dipaphragmatic problems from muscle issues, not nerve damage which is what your husband suffered.
I am sorry that he is so short of breath, unfortunately this can happen with unilateral paralysis. How are his lung functions? (PFT's) If his volumes are low that could explain his voice going in and out. Just reaching though...I am most certainly not an expert or doctor, but live through the problems with diaphragmatic weakness/paralysis.
One thing that they can do if the symptoms are severe is what is called diaphragmatic plication where the surgeon essentially tacks down the affected side so that it cannot move up into the lung cavity with each breath. Normally, when you take a breath, the diaphragm moves downward. When it is paralyzed, the affected side(s) move upwards which can make you breathless as it takes up space in the lung cavity as you try to expand your chest. This is something the doctors will do as a last resort though.
I hope that this helps...Sunny