Horse does a little hop to trot?

Hi everyone, I have an 18-year-old Standardbred I’ve been working with for about a year. We’ve made good progress, but trot transitions are still a big struggle. He almost always does a little hop/jump into the trot and falls over his right shoulder while trotting. If I try to correct his balance, he either drops back to walk or rushes off. Sometimes he gives a few perfect steps, but it’s not consistent.

If I ask quietly, it takes forever for him to transition he’ll just start walking faster and faster. If I use a light tap, he’ll trot but with a big hop or he bolts. Once trotting, any attempt to improve balance makes him either break to walk or speed up, with only in rare magical cases he takes to correction well and take a few good steps. Left alone, he keeps trotting but leans over the right shoulder. Same on the lunge and under saddle.

Medically: last spring he had a back left knee issue (likely from slipping), which was treated. Follow-up showed no lameness and X-rays of knee, hocks, and neck were clean (no arthritis). Vet, physio, and trainer all think it’s balance-related, not pain. He does have some back tension but that responds well to the physio and massage and shivers on the right hind, but the vet wasn’t concerned by the shivers. Ulcers were treated earlier this year and seem resolved. I’m wondering if anyone recognizes this: could this really just be balance/training, or could something medical still be hiding? Did your horse improve over time?