My gelding was similar- very balky to start, and usually after he had a poo, he clicked on and off we went. Thats how it started, and while that was really his only symptom I had all the things checked that you mentioned, and nothing was adding up. But it eventually got worse to where he wouldnt move under saddle unless I sat waaay back like a cowboy on my pockets. Spinal xrays showed severe bridging of the underside (ventral) of several thoracic vertebrae- basically everyone we could see clearly on the field xray there was that bridging. The top part of the vertebrae looked fine.
Ultimately I had to put him down at age 11, as he also had other bits of worsening arthritis in every joint we looked at practically, and also had cushings. He started having trouble going down, would not lay down in a stall, but if he did manage to go down for a roll outside, he’d shoot up and take off with his butt tucked like something was stinging him. He also started to trip and his hind legs would fall out from under him when he was moving.
I wish I had done the xrays sooner, and quite honestly now I do them on every horse I get just so I know what is going on.