My husband has had a VNS for over 5 years for epilepsy. It was a miracle for him. No more seizures. I asked him about the breathing issue to see if it would help with what you're going through. For him when it goes off it affects his vocal cords(the wire runs right next to it) and he said that's where he feels the constriction.
It did take him awhile to get used to and even recently he taped a magnet to his chest to turn it off for a week because he had a bad cold and it was irritating going off with the cough he had. After having it off he had to ease back into having it back on again and get used to it going off all over again. It took a few days of turning it off and on again with the magnet but now back to normal.
We've been following the research since he got his into it's use for depression so I hope it can work out for you and help
Jeanne