I wouldn’t go so far as to say race bred QHs are " known for an unlevel head". Had several racing bred QHs and Appendix (including my first 3’ Adult Hunter who had a tattoo indicating he raced) over the years as well as OTTBs and none were any more or less crazy then any other breed.
IME, erratic, unpredictable behavior is largely related to physical issues, not mental defects. Some of those physical issues are due to injury and/or hard work, some are hereditary. We now know of things like Kissing Spines and neck arthritis and better diagnostics are revealing things we can’t see that hurt, within the spine, hoof or joint for example.
What do this mares most recent X rays show and how do they compare with her PPE X rays? How long have you had her?
Many mares are spookier and over reactive due to hormonal issues, that’s why many prefer geldings. Have you tried her on Regumate? Have you tried her on Bute for a week to see if it is pain related?
If you prefer to go the supplement route, products containing Valerian Root usually work better, think Valium on that one. However with no regulation, amount in a supplement can vary so it can give you inconsistent results from batch to batch. Pharmaceutical drugs are a better choice and there are several frequently used as long term tranqs.
Consider mares overall are more intuitive then geldings. She knows you get frustrated with her, maybe hate her and will react and respond to you accordingly. Doubt anything will mask that. Can your trainer help you out at all with a solution?