Confirmed that instead of figjting kukui every time you go to the elite four you fight new trainers challenging you for the title each time.

>confirmed trainers so far
Gladion
Hau
Kukui
Hapu
Sophocles
Plumeria
Molayne
Ryuki

As to whether or not this is the full list is unknown. I imagine other important characters like other kuhunas and guzma might challenge you as well. It might be that some trainers are exclusive to being fought at the battle tree and others exclusive to being fought as title challengers.