I went out there today with a view to trying something else. I thought I'd first try to see if I could drive her past the scary things on a lunge line, as you're far more powerful driving a horse from behind than you are on its back. That would either (a) improve things or (b) she'd have such a meltdown that I'd know we'd have to try something else. After a couple big spooks, she settled down and went past the scary stuff without much trouble. She would not spin and wheel towards me carrying a lunge whip, so she found the chutzpah to go forward past the object.
I told her owner I wanted to try her in the long lines and owner went off and scared up a second lunge line. I set her up in the long lines and after a moment's confusion as she realized this wasn't plain old lunging, she got a brain transplant. Soft, obedient, "yes ma'am" to everything I asked, working in a lovely, consistent outline. No spooking at the stuff she normally spooks at. No being distracted by stuff going on around the barn. No reactivity or refusing to go or spinning. For the first time ever with this horse, I felt we were on the same team.
So riding, especially in the arena, is our issue. It's either a pain thing or she just feels uncomfortable and unbalanced with it (owner assures me she is much better on a hack). Or perhaps she just wants a career as a driving pony. I'm going to long line for a while and use that to build up muscle and balance, then revisit the riding. If she's still a spooky nutcase, I'm going to encourage the owner to call the vet. But the horse was happy as larry to long line, so that's what we will do for now.