I worked with a child with this problem. Sent him to an ENT and they found nothing. Ended up using the See Scape (I believe it was called) so he could see what happened when he was having the nasal emissions. He also began fronting his tongue, which appeared to decrease the "snort" . He still has a slight frontal lisp but no more nasal snorting. It was very strange indeed!
Thank you for sharing!