I would follow instructions from Dr.Parks. I personally experienced choking and aspiration. I was tested by an ENT with years of experience as a Dr. The flap that stops food and liquid going into the windpipe was relaxed. I had therapy and was diagnosed with sleep apnea. The age is in question here, because these symptoms are present with a stroke patient. Good Luck with proper diagnosis.
Based on what you've told me, it's hard to say exactly what the problem is without a thorough examination. It does sound positional. It's also somewhat unusual in that most of the time, the reverse occurs. Does he have problems breathing in or out when sitting up? What kind of imaging studies did he undergo? Did anyone examine his upper airway sitting up and lying down? Usually an ENT will do this. At this point, the obstruction can be anywhere from his throat to his lower windpipe.