Any improvement with netting the hay?
It’s been a lotta years since my horse was quietly choking with frequency, but what I recall about that period was that she was a very careful eater. I figured that she’d dealt with it long enough that she knew what worked and what didn’t to “manage.” It doesn’t seem to be a stretch to say a horse might be less interested in hay if eating it is causing discomfort going down. They’re no dummies, they figure it out when something feels bad.
Hiatal hernia in horses does seem QUITE rare–that paper is apparently the first report in literature, and was published in 2020. It might not be a bad idea to print & bring with you to your appointment, so everyone is on the same page.
It is really interesting that it was reported in a Friesian. Is there any chance at all your horse is part Friesian? Non Friesians can certainly have weird swallowing disorders, too, but if she might have some Friesian blood, that does seem like it would raise some eyebrows.
Once you have the imaging, it wouldn’t be very costly to send it out for review to whoever is super interested in swallowing stuff. Another set of eyeballs (esp without having to haul the horse anywhere new!) can be really useful.