This will sound stupid. But if you press your thumb onto the center of your hand, and then close the others fingers around and press, you'll suppress your gag reflex.
This saved me when I had to take some medicine as big pills. Without this trick they often got stuck in my throat, and it could take me minutes to properly swallow. With the trick? No problems anymore.
I heard something like this the other day. Is it the same thumb as the palm? 'Cos I can't press my right hand thumb to the palm of my right hand very hard.
Ooo, does that have something to do with how moving your arms like that flexes muscles around your throat? Is this an autonomic process like flexibg the timpani muscle when chewing?