On the note of some remaining back soreness - having correctly-built muscle often prevents, helps, and can even solve various areas of soreness. Often people think their retired horses, or horses that haven’t been in work for a while, don’t need chiro and such, because they’re not doing anything. In fact, I typically find that those guys need more frequent work or have more “issues” pointed out during adjustments than those in regular work.
For example, I had a barn-mate who maybe walk/trotted her horse for 20 minutes three times a week. Every chiro adjustment the horse was “out” like, everywhere. Meanwhile, my girl when in heavy dressage work six days a week (she was schooling 3rd level, one day per week was an hour of only walking, one day was hacking/hills) barely had anything “out” during her adjustments. Smidge in the shoulder (where she holds her tension) and TMJ (again, tension, she’s a nervous type), that’d be it at most.
So, if it were me, I’d start OPs horse back with only walking. Hand walks or on the lunge line for 20 minutes three days a week for a week or two. Then four days a week. Then five days a week with up to three of them under saddle. Then all five under saddle, 30 minutes. Then 40 minutes. Admittedly I typically slower than many others do with rehabbing. But I’d be only walking for at least two months.