Opening the throat does not make the mouthpiece less stuffy. It makes the "targets" or slotting looser - a big advantage for Bach C trumpets with the high third space C, flat 4th space E and sometimes sharp top of staff G.
I have found that "stuffy" generally means that I can't hear myself well. Even with my current setup that is wonderful in churches and concert halls, when I play outdoors with little reflective surfaces, it feels stuffy. Experiments with the 1 1/2C back in the day, had me push the tuning slide in further (making me slightly sharp) and then relaxing more when playing. After a short while, the more relaxed chops resulted in much more open sound and far less embouchure tension - great for more endurance and a better upper register. In addition, articulation got easier where my face muscles were doing less.
I would suggest experimenting with pushing the tuning slide in so that you are maybe 10 cents sharp, and then "lipping" everything slightly down. For me it was like pulling the cork out after a week or two. 10 cents is not much work to compensate and I found it much easier to hear myself with the "new" tone.