The music teacher was unenthusiastic in his response. His specific concerns (materials and where it was made) didn't seem totally justified (it's made out of various metals and was made in the U.S.A.) but that gave me pause.
I went to the recommended used-instrument store today, looked at a few trumpets, decided to go ahead and get one of those. It's in pretty good shape and the store has a good return policy.
Basically, if the music teacher nixes it for any reason they will either fix the problem or if it's unfixable, take the instrument back, full refund. If the music teacher is fine with it but sozlet changes her mind re: playing the trumpet, or if we don't want it anymore for any other reason, they'll buy it back for 50% of the cost.
Hope it's the right decision, I went with the mob on this one (it's what almost everyone does for band if they don't already have access to a used instrument).
They cleaned it at the store, we boiled the mouthpiece for good measure and she's now doing her best dying elephant impression. Super incredibly loud dying elephant. Whoa. I can hear it QUITE well, which never happens. And I thought I'd be happy that I wouldn't have to suffer through beginner's tootles.
Oh and thus far the braces have been a non-issue, yay.