You need to spend more time with him on the ground. You also need to use more body language to more effectively communicate with him.
When you're lunging or working in the round pen, you need to make sure your body is aligned so that you're BEHIND his drive line. The drive line is the line at his girth. You need to be sure your standing behind that line, and facing/looking at his barrel. If you step toward or turn toward his head, you are inviting him in to you.
Since you know he's going to turn in at this one point, you need to be extra careful about where you stand and look, and push him more with your whip as he approaches the spot. Drive him forward with your whip, really pull your shoulders up and back, and radiate your energy toward his barrel and hip. Step toward his hip/barrel if you need to, if you see him start to turn in. Pop the whip and say "OUT." Praise him with a "Good boy" and a softening of your stance when he goes back out or stays nicely on the circle.
For saddle work, I would highly recommend a ThinLine pad
. It will increase comfort and eliminate any possible minor saddle fit issues you may not realize you have. Most trainers do not have professional saddle fitting training, so they often miss a small issue that your horse may think/feel is a big one. I would go with the ThinLine Contour pad. Here's an Australian distributor of them: ThinLine Contour Pad
Also make sure your saddle is properly placed, so the front d-rings are 2-3" behind the back edge of his shoulder blade.
When riding, be calm, be relaxed, and expect him to act right. When he goes down and begins to buck, YANK his head back up and KICK him into a tight circle, yelling "QUIT THAT". Trot him on a tight circle until he submits to you, pet him and tell him "good boy," and go on with your ride. Rinse and repeat, changing directions of the circle each time, until he quits bucking.
For standing while mounting, you just need to be more persistent. When he moves, swat him on the chest with a whip and say "QUIT" and back him up to where he was. Pat him and tell him "good boy" when he stands nicely. I would use a mounting block to take some of the strain off of his back when getting up. He may not like his withers being pulled over.