Sorry I didn't read all posts so if I restate something my apologies. But way back when, in highschool I wrestled. I also have rode horses my whole life and felt I was always well balanced. Anyway to improve our balance for wrestling me and a couple boys took gymnastics(and got made fun of). But I was amazed how much better my balance overall got, especially in my riding.
The one thing that was funny was when our gymnastics instructor asked us how we felt our balance was. I told her really good, well she grabbed my foot and hiked it up in the air to the height of my head. I hit the ground like a ton of bricks. Never boasted to her again, but I have appreciated all I learned very much. I think a lot of it is like yoga too so give it a try.