Saving screen buffer for instant replay - ALA Towerfall

I want to make a multiplayer game. When a round ends, you will be able to see an instant replay of the previous 2-5 seconds. Oh, and the game has a fixed screen/camera.

The feature is similiar to what the game Towerfall has (see this document :https://docs.google.com/document/d/1UtZZVXgR8TTB67h3HgNvluUIMGvyCgW2dSWflTiUgJU/mobilebasic?pli=1)

In short, the game should constantly be recording a buffer of 2-5 seconds gameplay as a series of images. Then, when the game ends, it will display this screen buffer (and maybe allow for export as animated GIF if possible).

How would I implement this in Unity without hurting the overall performance of the game? I have looked into the GrabScreenshot function, but it seems to be too slow. In fact, I don't really need to save the images as individual files all the time, only just in the end of the game.

Thanks in advance.