I've thought the same thing for many years. I think a sports physiologist could help him. I couldn't stand the Dodgers but a did feel sorry for Sax, it was hard not to. John Smoltz went from a very good pitcher to an elite one with the help of a SP.
I've witnessed mental toughness on a personal level. My daughter played on an elite travel team that competed on the national level and was the best 2-strike hitter I've ever seen. She told me she preferred being down in the count because it made her focus more. I remember one game where she fouled off 9 straight balls before driving a double in the gap. She was also the best bunter, whether it be a suicide play or just moving runners in a close game. When many other girls got 2 strikes on them, you just knew they were done. You could just see it in their body language.
All these years later and I am still envious of her mental fortitude. She never ceases to amaze me on how strong she is.
Sorry about the long personal tangent, but I do think you're on to something. I do believe his problems are between his ears and a SP is definitely worth a shot.