Start looking. So many options. Arab x with a stock breed or draft(lots of nice arab/qh out there), tb x with stock or draft(tb x percherons are popular, as are appendix qh's), morgan or morgan cross, a quieter arab or ottb, a well suited qh, and the list goes on.
If bolting is your concern and you want something really quiet, look into the draft crosses, often they tend to be laid back.
I also question your use of the term 'advanced rider'. I've ridden most of my life, over a 100 horses, thousands of miles, mares, geldings and stallions, from 12hh-18hh(welsh, arab, draft, warmbloods and everything in between, except a fjord, I would like to try one of those), ridden dozens of thoroughbreds straight off the track, started colts, halter broke many horses, from weanling to mustangs straight out of the foot hills, to a 17.2hh Clydesdale stallion. I've competed in team penning, competed in endurance and CTR, ridden some crazy mountain trails, and jumped a fair bit for fun. I would consider my self intermediate. The more I learn the more I realize how little I actually know.