Hello~ I have a bulldog that has this. Why are they doing the barium test? Is this to confirm that he does in fact have it. The xray should show a huge pocket that is not allowing his food to go to his tummy. This is the reason they suffer weight loss and they throw up their food. I know about the chair but I have never got one. I feed my dog every morning in his bowl holding it up in the air at an angle downward so the food falls to the crease of the bowl and then he scoopes it out with his tounge. The problem with the throat being narrow kinda of takes care of its self because when you feed them the way I do you only allow then to eat a little at a time. If they get to much they will turn blue on their tounge. But mine has managed to keep swallowing till he gets it down so then I cut back on the portion I pour into the bowl. When he gets done he coughs a little but it gets the food past the sak and into the tummy. You should do something to keep his head up after he eats to ensure his food goes down after eating. So what I do is continue to hold his bowl in the air and he keeps his head up and then hes good.
Hope this helps