It would be unusual for critical illness polyneuropathy to involve the vocal cords. Other possibilities could include injury to the vocal cords secondary to prolonged intubation, or an underlying muscle disorder causing muscle weakness. Based on your statement the vocal cords move, but slowly. Does he have any difficulty with breathing. If he does not breath properly he may also not be able to articulate properly. I hope this helps, good luck.
I am a speech therapist, and am only offering a guess at what could be the origin of your husband's speech (actually really what we call a language) problem. With all that he has been through, it is likely that at some point there has been a lack of oxygen to his brain causing anoxia, which results in all kinds of cognitive and language problems. OR, he may have suffered a stroke as a result of a number of the illnesses and procedures you mentioned. A stroke, by definition, affects the brain. If it affects the language center, he would have aphasia, a condition that results in varying degrees and types of language difficulties. I hope I didn't alarm you, because of course I cannot make a diagnosis by email, but these are some of my thoughts. Good luck to you both.