Firstly, I'd like to say how much I love the Competition Arena. Some people don't like it because it's random and they feel they don't always get a "balanced" team. But that is what I love the most about it. You must learn not only to adapt to your oponent, but to your own team as well. No battle is ever the same as the last and you never know what kind of group you will face next.
My suggestion is to build a Tournament arena with the same ideas. You should be able to earn Fame from this, but not take the Favor of the Gods.
Before you can begin playing, each time you must go through 4 tests SOLO (Think "Wardens" in HoH). After you complete these, you must also go through 2 more with your random group you have aquired. After that, you'd be ready to start earning your fame

Battles would consist of 6 vs 6. The fame system would follow the same rules as the Tombs.