I also see some slight "upside down" muscling to her neck in that picture, although she does have her head up and slightly angled, so that may or may not be an optical illusion.
I would definitely go back to installing brakes. Aim for only using your seat, weight, and leg aids. Really think through your process as you ask her to slow down. Give her a good connecting half-halt first; that will get her attention, rebalance her, and tell her that a bigger change is coming soon. I won't go into detail on half-halts here, as the topic has been beaten to death on other threads. I know it sounds dressage-y, but correct half-halts and the effects that they have on our horses are extremely valuable to barrel racers and other disciplines, too. When you do apply your slow down/halt aids, be sure to exhale, relax, and feel yourself melting into the tack. Don't take your legs away from her sides; you want them "in neutral," neither asking for movement nor "floating." Your legs are there to support the good positioning that you've gotten from an effective half-halt that will make it easier for your mare to slow down and stop quickly and smoothly.
Start at a walk, ideally in a controlled environment like an arena or roundpen, although an open field without any hazards (random fence-posts, woodchuck holes, etc.) will do in a pinch. The idea is that you want to let her go, and focus on her speed. Take all steering out of the equation. Get her moving out and forward at a walk; marching and stretching. At first, leave your reins slack. When you're ready, give your half-halt aids, and then ask for a halt with everything except your reins; Relax, exhale, melt into the tack. Stay loose, and allow her to come down into the halt or lower gait -- sometimes riders stiffen up when they just think "down," and the horse drops their back and throws their head to avoid a "loud" seat. Think of the whole process as happening as you say "Steady (half halt here), and Whoa (or whatever downshift degree you're looking for)."
If she responds, great! Reward her -- if she really prefers to move, put her back on a forward walk and rub her, and if she is really relaxing and telling you that that no-reins stop feels good, rub her at a standstill and let her "bask" for a moment before doing it again. If she keeps on sailing, maintain your "whoa" aids, pick up on one rein and spiral her down. Don't be abrupt about it, just calmly spiral her down until she stops her feet. Surprising her can off-balance her, which can be downright dangerous if you're at speed and try to sharply shut her down this way. The steady, firm, one-rein, spiraling action should prevent most of the head-tossing. Rinse and repeat. When she starts "reading your mind" at the walk, try it at the trot. When stopping/downshifting without reins becomes her default, you can start to reintroduce a little contact with her mouth and using the reins for what they are really intended for; guiding and positioning the shoulders and forehand around those barrels, or through whatever other movements you want to do.
Most horses will surprise you when you start this exercise -- that lovely, relaxed downshift is right under the surface, if we ride in a way that allows them to show it. It looks in the pic like you're using a Wonder-Bit or similar setup -- the exercise above works best in a simple 1:1 pressure ratio snaffle bit, because when you do pick up on the reins it's one side at a time. The combined leverage and mild gag action of a Wonder-Bit can add unneccessary confusion to the mix when ridden one side at a time.
You might also look into some long and low exercises to get her stretching from her haunches forward, getting really round through her whole body and getting some true "vertical flexion" of her whole body, and not just her face. Again, it sounds dressage-y, but it'll pay dividends on your barrel times when she starts listening and rating off your seat, and carrying herself more efficiently.
Hope that's helpful to you! Good luck!!