Best Role to Carry Low Elo

Anything other than support. If you want to climb, you should really just play whatever you have the highest winrate with.

IMO, jungle and mid. Both of those can affect the game faster than any other role. Splitpushers top can work well, and good, self-reliant ADCs. I'd still put my money on JG and Mid. JG can have the game out of reach before 5-10 min. Mid can hit 6 and roam bot and pretty much seal the game at that point. You hit 6 on Fizz, roam bot, get double kill+turret+dragon, you pretty much win the game at that point.