At her age & considering what you've noticed, I think you're on the right track except for doing circles & stuff with her *unless advised by a bodyworker*. Most certainly a well fitting saddle that doesn't pinch her is a start, as well as not over tightening the girth. I'd get a good practitioner to come give her a treatment & advise you whether there's any damage from badly fitting saddles that needs to heal before saddling her again.
Hoof care is probably no 1 issue with tripping - long toes, high heels, thrush or otherwise weak heels, thin soles, etc. I imagine she's a no. 1 candidate for most of those, being a shown TWH who's owners cared to sore her. Dentistry/bit problems can also cause problems such as tripping, not to mention the hands on the reins.
Weak heels - check (her thrush was mainly in her heels)
Thin soles - check (Durasole and Keratex have improved this a lot)
Dentistry/bit/hands on reins... interesting. Probably not the problem, since she's been recently floated, and I'm very light on the reins, but I'm very curious. I never would have thought. Will you please elaborate? I assume it has to do with carrying the head in a way to avoid the bit, which then hollows the back and causes poor movement of the legs?