I’m coming in late with some observations. There is a difference in body condition from day 1 (sale video) to now (pasture video). He looks like a different horse, but in both videos he is unsound. What was the other place’s management like, can you replicate it? This is a relatively inexpensive first step.
There may not be just one thing causing all this; it may be compounded by multiple problems at once. Sometimes there’s not just one answer, but all issues are exacerbated because they’re triggered by one thing being set off.
Has anyone ever looked at this horse’s feet critically? Have his feet been done since you bought him?
I don’t know how four vets could think that this horse is sound off of the videos you provided with your trainer riding. He wasn’t sound in his sale video - he is bilaterally lame up front and behind. The abnormal tail carriage and the uneven strides behind were there from day 1 of the sales video. My first impression of this horse was he moves like a classic chronic navicular case and his feet are bothering him on top of whatever neurologic component is there. Horses clinically diagnosed with navicular changes share some overlapping symptoms with what’s evident in the sale video: stiff tail, weak pelvis, toe shuffling, bilateral lameness, etc.
None of that would explain the weirdness you’re encountering when you get on him, which is a separate, far more serious issue entirely. EDM, neurological bladder, tumor in or near the spine are definitely possible. These are more serious and depending on diagnosis and finances, either untreatable or come with weighing QOL as well as safety of all that handle them. Certainly no one would fault you for any decision you make at this point in your journey. You are in an unenviable position with very little answers after thousands of dollars in diagnostics. It’s a crappy place to be in.
Good luck and hoping for the best possible outcome for Jasper.