You're going to have to define 'reasonable expense'. The absolute cheapest route would probably be to try a 1.4x extender. You can find a the 1.4x ii for $200 or the newer 1.4x iii for $350-$400. That would put you to f4, though, which isn't pretty on a 7d at night. If you buy one used and don't like it, you can probably resell it and nearly break even.
For day games, the 100-400L is a mighty fine lens. Won't help you at night.
Personally, I'd be looking at a 300 2.8 variant if you are serious. That will set you back anywhere from about $1300 - $7000 depending on how you want to get there. The Sigma 120-300's probably offer the most 'bang for money'. I'd go for a new 'OS or OS Sport' version if you can swing it, but the non OS DG version certainly is more than capable. Canon 300 2.8's start around $2k for old beaters and start going up with newer models.