I’m not your veterinarian and this post is worth exactly what you paid for my opinion. However, I have rehabbed an SI injury (trailering out every week, then two weeks, then month, then 6 weeks to a specialist vet/chiropractor… it was a complicated confluence of multiple injuries all sort of secondary to each other.) I will say that my experience, and that of the above vet, is that horses with active SI pain tend to be more comfortable at the canter than at the trot. If the horse is happy at the trot but uncomfortable at the canter, I start looking at the stifle or the hocks. I mention this specifically because you came from a program that injected first and asked questions later. If the problem is in the hocks, your horse is a little young for arthritis in that joint, but it is not out of the realm for a horse who has had a history and this may actually offer him significant relief. (So would Legend, oral HA, MSM, and all kinds of other things you can try first.)
All that is to say- it sounds like you’ve found a much better situation for him, I’m glad you have the vet on the way, I’m really glad that your vet travels to your farm so you don’t have to schlep the horse an hour each way as long as I did and keep an open mind about what you hear!