I had good success by following up my GI doc appointments with a trip to an ear-nose-throat doctor. Your coughing, mucus, and burping actions are similar to some of what I had going on. When there is a problem with the voice, as you clearly have, an ENT doctor will know better what may be going on than a GI doctor, whose study begins with the esophagus, not the throat (I didn't know!). If a person has LPR, reflux into the throat, that is usually treated a bit more aggressively with medications than standard GERD, from all I've read and been told.
Mind you, I didn't have the esophagitis and all the abdominal symptoms you have, so I'm not trying to diagnose you. :) However, I do know that when the voice is affected, and when it just cuts out as yours does, a thorough study of the larynx is a smart idea. It's certainly something to bring up with your GI doctor tomorrow.
Good luck! I hope you get some relief *soon*!