after seeing the video… i’d be checking her hind end, her LH especially. have you had the saddle reflocked recently? at minimum, she is very tight and crooked. hopefully it is just something that maybe needs an adjustment over actual HS…
it doesn’t really look like HS to me. she may have just gone better in the indoor because it was after she was warmed up.
in my experience, HS never really ‘ramped’ up - you said it was first only at the canter, but then later on developed at the trot. to me that is typical of a progressive discomfort/lameness - especially if the flipping starts at the canter.
in the HS horses i dealt with, it started like an allergy and wasn’t confined to only undersaddle or in work. IME at least the first symptoms were during stall time - runny noses, rubbing their nose on things, head-shaking, eyes weeping – it gradually turned into tossing their heads during turnout, etc. it always manifested whether or not they were U/S and the fact you are seeing it exclusively U/S would make me think it’s a soreness somewhere over HS.
has her front hooves ever been x-rayed?
i think sometimes you also have to look at the smoking gun - why is she able to get her tongue over the bit? i’d be putting up the bit or switching to something else while you investigate if there are any other causes. does she root or is she extra fussy with her mouth otherwisE? those can both be symptoms of SI soreness and hock issues.