@anon4362788, I think you can level up your humming solution.
Whilst humming, place your hand gently on your throat and tilt your head up and down. Keep your eyes open whilst you do this. Try to find the angle at which your throat is the most open, with the least scratchiness or irritation. Try it without your hand on throat too.
Once you’ve found the right angle, remember it. Next time you feel like gagging, hum like you normally do, but with your head at that magic angle. This should create optimal openness of the throat. Eyes should be open, but hand on your throat is optional.
Growling like a monster might also be an upgrade from humming.
If I get even just a tiny bit of dust in my throat I’ll gag and I’m likely to throw up. It used to be a big problem at work. I ran for the door many times to get outside to throw up away from people. I found the simplest solution that works is a piece of butterscotch candy. It produces saliva and coats my throat and works about 95% of the time. I tried other hard candy but the only other one that works is a piece of Jolly Ranchers. I always keep 3 or 4 pieces of candy in my pocket for emergencies. I buy a three lb. bag of butterscotch candy off of Amazon about every three or four months.
I used to gag from dry mouth caused by cogentin. Especially in the morning and I threw up every now and then. My doctor had me stop the cogentin and now mornings are fine.
IDK if the caramels would work. Butterscotch just has the right consistency while most other candies I tried produced “thin”, watery saliva. Butterscotch candy just has enough consistency to coat my throat and prevent gagging. And it tastes great.
!