She sounds like a repeat of my son. I figued since he counted to ten at 18 months he would surely want to not want to sit in his own stool. WRONG!!! I tried everything you have said (with the exception of taking away toys) and nothing worked.
At his third birthday, he became very ill. It was three weeks of vomiting and diarreah and it ultimately put him in the hospital. Needless to say all of our potty training efforts were completely ditched during this time. The doctors said it could take a month or two before he GI system recoverd and we were told by our doctor to not try potty training for another month at least. A week after his last episold of vomiting and diarreah and no pressure from us, we noticed one day that his diaper was dry all day. We were worried there was something wrong, but he said, "No, I go in the potty now."
Moral of the story? Ask them to try for every hour or two, but don't make a big deal of it like I did.
I think it is possible that so much pressure and expectaions are put on kids to potty train early that it could actually make them afraid to fail. I know it sounds crazy, but think about it. You said she is really smart, hu? This is probably the first thing you have seen her "fail" at. The whole goal is to make it her accomplishment, not her failure.
I hope you can ditch the diapers soon....
Liz
P.S. Since it is winter, try putting adult tube socks on her as leggings with a shirt but NO underwear or pull-ups. Keep a potty in the room with her(we used BabyBjorn~$11). She may just think it is an inconvenience to take off her clothes and walk to the bathroom!
P.S.S. I couldn't help but notice that you classified this question under "discipline and behavior". Try not to think of it that way, instead, maybe "development".