So from my understanding rank doesn't mean a whole lot and is not tied to matchmaking.
What I suggest is make Elo (whatever that is) the new rank system so players can see how they stand.
We already have a season pass so it would make sense to take the rewards from the rank system and add them to the season pass. The rewards would need to be balanced around the fact that you wouldn't be able to double dip from ranking up in multiple game modes.
Or add the rewards as different milestones at the end of the normal season pass for people who really grind the game and as extra incentives for anyone completes the season pass early.
This would eliminate the need to hand out rewards at the end of the season and streamline the game a little.