I have not read all of this thread, so I don't know if someone has already brought this up or not. Although sway back can be genetic, is it also nutritional. If he did not get the right nutrition when he was little little, it will cause a sway back. I used to work with a rescue that actually started actively picking up horses who had this kind of sway back and breaking them to harness so they could have a productive life - but some of those colts were 20 times worse than your boy.
I also knew a person (not goign to call her a friend) who didn't think anything of poor nutrition for her mare in foal, of poor nutrition for the foal, or startign the filly under saddle at 18 months old. Needless to say this filly had severe sway. Eventually I convinced her to part with the filly at about seven or eight years of age. By this time, constant malnutrition had dropped her back almost a foot - and she rode that horse hard too.
I worked with the people who got the mare on techniques for stregthing her back. The first step was better nutrition and putting 300 pounds of weight on her. That whole time, they did TTouch exercises to get the mare to lift and round her back. You do this my digging your fingernails into the centerline of the belly. It is not a good sensation and the horse moves away from it, lifting and rounding thier back. Please do a search to find out exactly how to to this, as I have only done it a couple of times.
Anyway, it took about a year and a half but they brought that mare's back almost streight! For the first time she could wear a western saddle. It is possible to do a lot towards 'fixing' a sway - though his back may never be as stong as it should have been.
I hope this helps. He is beautiful and very lucky that he found you. Pleaes give him a hug for me!