Hi A.-
I don't know if I can add any advice here, other than I feel your pain. My 2nd daughter, who is a middle child, was - I swear- just born angry.
By herself she is a really sweet, helpful girl. Add her siblings to the mix, and the tantrums run plentiful. She too is 6, and starting 1st grade.
Just this morning I had to remind her that we needed to take a bath. She opted out last night, so we had to do it this morning...well I heard all about how she didn't want to do it. Stomping, shouting at me, huffing and puffing upstairs.
I also see the quick "oh, I can't do it". So quick to give up at the littlest set back. No perserverance at all sometimes.
I've often asked her "why are you so unhappy??" Not that she can answer, but that's what your heart feels like asking. I'll be anxious to read your responses.
Sorry I'm not more help!
A.