The 3rd and subsequent rounds will go quicker than you think because your in the game and your not looking at players. Your merely selecting the next team on your list and then sorting and taking the top player and signing him to a MLC. 4 fast clicks!
The second will go fast as well except if you see an MR, you will hopefully open his player screen and maker sure he doesn't have 5+ endurance. If he does, skip him and remember his name so you can keep skipping him until the 3rd round.
Trust me, this will go fast and won't be as much of a bother as Browntown sending me 137 minor league cuts in ALPHABETICAL order by name instead of the proper positional order!!! I friggin' needed 3 tylenol, a percoset, and two Sam Adams... after that.