Just keep doing it and try to relax with your throat open. It's the gag reflex. Your body will eventually realize that you're in no danger of choking and will quit reflexing to try to save your life. If it really won't eventually relax, you could be overdoing it.
What happens if you ease off just enough to stop the reflex?
Maybe you could go to that point for a while and then gradually open up a bit at a time until you are able to stop the reflexing.
There is a tendency for many to have the gag reflex when going through the passagio, but it sounds like you're saying that you are experiencing the gag reflex almost anytime you are using open throat. That's not natural, so I'm suspecting that maybe you are overdoing it.
We tend to gag when we put a finger down the throat. That is to protect us from something going down into our lungs. That's what the vocalis is for, as well. Our vocal cords are the last line of defense to keep foreign objects from dropping down into the interior of our lungs. You may be stimulating the same nerves that get the reflex if there's a finger back there.
You get that feeling if you touch anything to your uvula, also. There could be something going on that is just tickling that gag reflex. I have a litte angled medical mirror that is lighted that I can stand in front of a mirror and see my vocal cords with. The only problem is that if it touches my uvula, I feel like I'm gonna hurl!
I think you just need to relax. Experiment like you said, without singing, and see if you can tell where the overstimulation is originating from. Try for a more natural pharyngeal posture. You don't feel like gagging when you yawn, do you? Your Open Throat position should be no more open than that. Are you feeling like you're about to swallow something evil when your throat is in that position?