she could be like my horse Chief, his old owner tried him in a bit but he was a head shaker too, the guy had his teeth check (so have I) he just hated the bit, now he's in a hackamore and he does really good. I wouldn't suggest a hack right off due to her being trained to run and you have more control with a bit. My OTTB mare required a long shank tom thumb type bit, I'll try to get a pic of it today. Also used it on my OTQH and she did awesome in it aswell.
"A horse can lend its rider the speed and strength he or she lacks, but the rider who is wise remembers it is no more than a loan." ~Pam Brown