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I have had the same problem and have been working on it for years. I can also fit a pencil between my teeth so I guess I'm open enough. A bigger mouthpiece has hellped a little, but the only thing that has really worked for me is to work with a drone to re-learn how the pitch should sound and tune to that. At least the tuning slide stays in the horn for me now. Some horns (old King 2341 for example) I can't play in tune at all. I have always needed to play horns with long tuning slides. YMNV.

I often have students bring in carrots cut into 3/8 inch pieces. Then I have them put a carrot cube between their teeth and play. Carrots work great because if they do swallow it... no great harm done. The chunks are too large to go through the mouthpiece.