What about the Scout? The fourth member of the staff...
I was actually just coming here to post this, but looks like I was beaten to it.
Implementing a scout as a 4th staff member could make a lot of sense... the levels could be roughly matched to the 5/10/20/40k scouting prices we have now, and would allow specialties to address some of the issues that have been raised in this thread.
For example, maybe you get a Frequent Flyer specialty, where your scout travels as much as possible, getting a lot of 1 visit scoutings, but very few repeat visits. Conversely, you could have an in depth scout that would tend to spend more time at each scouting visit, increasing the likelihood you'll get 2nd impressions of players (whether good or bad players), but decreasing the total # you can scout.
Plus the idea of having a scout as part of the staff makes much more sense than having it included in the Training menu.