Was able to get a press/field pass for a professional soccer game in mexico last week. Bought a tamron 70-300 VC its sharp and the AF is very fast. The only focusing issues I had were my lack of experience with my camera's AF system as well as it was my first time shooting a soccer game which can be tricky. You can probably find one on CL for about $275-375, but I think its worth the new price tag.
However, the lens isn't as sharp past 200, so with your need of a lens >200mm this might be an issue if you need super sharp photos as well as reach. IMO its the best non L zoom, and if you only need if for baseball and you aren't getting paid for it then I think its the best option. Also, the zoom ring is reversed, but you should adjust pretty quick.
If money isn't a factor get the 100-400L II better IQ and reach.