Is there a way to make the Elven Accuracy feat work with the second benefit of Great Weapon Master?
Elven Accuracy (XGtE, p. 74) says:
Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.
The second benefit of Great Weapon Master (PHB, p. 167) says:
Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a – 5 penalty to the attack roll. If the attack hits, you add +10 to the attack’s damage
Boundary Conditions
Any official material (non-UA) is fine, as are optional rules like feats (obviously) and multiclassing.
What does not work
The Shillelagh cantrip lets you attack using Wisdom, but the Quarterstaff is not heavy.
Background
Champion Fighters could really benefit from an increased crit chance, and melee advantage is very easy to get.
Best Answer
The most optimal way to do this would be to play a Half-elf Hexblade.
Drow (PHB) & Shadar-Kai (UA Elf Subraces) come in second (+1 to Cha vs Half-Elf's +2), and other elves are still viable (just a little behind on Cha). You can start using a heavy weapon once you reach 3rd level in Warlock with the Hexblade Patron.
Hex Warrior (XGtE 55,56)
Pact of the Blade (PHB 107)
Also note that your attack cantrips such as Eldritch Blast and Shocking Grasp would benefit from the reroll as well.
Here are some ideas that come close but I don't think quite work:
Honestly, it makes sense that you are having a hard time using a heavy weapon without using Strength. This is part of the game balance that 5e sets up. If anything Hexblade/PoB breaks this balance by using Charisma with any weapon. Don't be surprised if you see Hexblade as the go-to for getting around balancing rules.