I played trombone with braces for years. You pretty much have to completely re-learn how to use your lips when you've got things on your teeth like that. IMHO the teeth are the "base" upon which the embouchure is built on, especially for high range. With things added, you end up stretching the muscles a bit more, so that may be why the double buzz was happening.
On the other hand, I have heard a story, which may be apocryphal, but it still is interesting. There was a budding screech trumpet player, and he idolized Maynard Ferguson. Everyone always wanted to figure out how he was able to have such an absolutely incredible high range. Well, this player noticed that Ferguson had a gap between his top front teeth. Maybe that was the secret! So he actually had orthodontic work done to add a gap like that.
He meets Ferguson, probably all hyped up to talk about the gap and high range. Then he notices that there is no longer a gap in Ferguson's front teeth. He asks him about it, and he said that he had it fixed. So, so much for that theory.
Whether the story about the trumpet player adding a gap is true, I have no idea. But if you look at older pictures of Ferguson and the more recent ones, he definitely did have a gap, and it definitely disappeared.
Sterling / Perantucci 1065HGS Euphonium, 1952 B&H Imperial Eb Tuba, and a bunch of trombones.