I know assumptions are bad but I have to make one here. I haven't trained any baseball players in the 60 but I have trained a lot of football players in the 40. 99% of the time I have a player with better game speed than his 40 time shows, it's because of his start. Either because of bad technique or because of what you mentioned lack of intensity causing a less explosive start. With a track coach saying his sprinting was fine it further strengthens my assuption that it's his starts causing the problem.
I can't give you much advise on working on 60 starts since they are so much different from 40 starts but search the site for the artical from PG about improving 60 times. It covers the starts. Good luck as an ex wide receiver I know how important that stupid stop watch can be to some coaches.