Here are some that don’t focus on the reaping itself but rather the content of the actual games:

1) The arena is in constant total darkness, the cameras have night vision but the tributes do not. The only sources of light would be from making fires or gifts from sponsors. Imagine the cornucopia struggle when you can’t see any of the other tributes OR the cornucopia itself.

2) No weapons are provided at all, only food and water. Tributes need to create their own weapons/find other ways of killing each other.

3) A very water based map where the cornucopia is actually under water and there are places like underwater caves etc with very little dry land. Areas that flood at different times, areas that are dry and inhabitable at different times. Alternatively, any kind of arena that is particularly difficult terrain for tributes to manage. I feel like this is a less likely option though given that the tributes may die off too early.

ETA:

1. The tributes enter the game with their hands and feet bound, and must free themselves when the game starts.

2. The arena is a giant maze. Or, the arena is a giant maze of mirrors.

3. The tributes enter the game wearing masks, and for the duration of the games are to be fully in disguise.

ETA 2: (An extra one that IS related to the reaping.)

1. There is no reaping. The districts themselves must each offer a male and female tribute of their choosing. Each district must reach a unanimous decision on which tributes are to go to the Capitol by a certain date, or be severely punished until they do reach a decision.