Welcome to GreyTalk and greyhounds. I'm sorry you're having to worry about one of your hounds so soon. No experience here, just some general knowledge about laryngeal paralysis and the esophogus because I'm a speech therapist who works with swallowing in humans.
Laryngeal paralysis is caused by damage to a cranial nerve, so yes, I suppose there could be some underlying neurological problem even in a younger dog like KK. But KK might have any one of a number of problems. I think LP dogs usually start choking or gagging when they eat, and you haven't mentioned that. Taking your vet a log of when events occur, whether anything is actually vomited (from stomach) or regurgitated (before it reaches the stomach), energy level, appetite, weight, how her poops look, etc., would probably be very helpful and help you work together to find a diagnosis.
What areas were x-rayed? Can you take a copy to your regular vet?
Welcome ear scritches to Jack and KK.