So I'm tweaking the 5e damage curve a bit.
At the core is making weapon damage scale like cantrips. You deal 1[W] 1-4, 2[W] 5-10, 3[W] 11-16 and 4[W] 17-20.
Next, Extra Attack becomes "you can sacrifice 1[W] damage on your attack action to attack twice instead of once".
Fighter EA 2 and 3 just add an extra attack (!)
So a fighter goes:
L 1: [W]+Stat
L5(EA): 2[W]+2Stat or 2[W]+Stat (1 attack)
L11(EA2): 6[W]+3Stat (3 attacks) or 6[W]+2Stat (2 attacks)
L17(EA2): 9[W]+3Stat
L20(EA3): 12[W]+4Stat (4 attacks) or 12[W]+3Stat (3 attacks)
this is a non-trivial damage bump.
For TWF, I'm thinking of rewording it as:
"You deal your attribute damage on attacks triggered by the light property. The bonus action granted by the light property can gain extra attacks from your extra attack feature, but must always be with the same weapon".
L 1: 2d6(7)+2Stat
L5(EA): 4d6(14)+4Stat (4 attacks)
L11(EA2): 12d6(42)+6Stat (6 attacks)
L17(EA2): 18d6(63)+6Stat (6 attacks)
L20(EA3): 24d6(84)+8Stat (8 attacks)
We then tweak GWF to read:
"When you roll an odd number on a damage die with a melee weapon held in both hands, replace it with the max value of that damage die".
This increases average damage as follows:
1d4: 2.5->3.5 (+1)
1d6: 3.5->5 (+1.5)
1d8: 4.5->6.5 (+2)
1d10: 5.5->8 (+2.5)
1d12: 6.5->9.5 (+3)
So Greatswords deal 2d6B(9) and Greataxes do 1d12B(8.5). Assuming GS:
L 1: 2d6B(9)+Stat
L5(EA): 4d6B(18)+2Stat
L11(EA2): 12d6B(54)+3Stat
L17(EA2): 18d6B(81)+3Stat
L20(EA3): 24d6B(108)+4Stat
Subtracting 2W from 2H we get:
L1: 2-Stat (Stat ~2 is even)
L5: 4-2Stat (Stat ~2 is even)
L11: 12-3Stat (Stat~4 is even)
L17: 18-3Stat (Stat~6 is even)
L20: 24-4Stat (Stat~6 is even)
ie, both have quite similar damage curves. 2H wins on an action surge handily, and has a nastier OA.
Duelist falls behind in comparison:
L 1: 1d8+2 (6.5)+Stat (~20% less than 2H)
L5(EA): 2d8+4 (13)+2Stat (~20% less than 2H)
L11(EA2): 6d8+6 (33)+3Stat (~30% less than 2H)
L17(EA2): 9d8+6 (46.5)+3Stat (~35% less than 2H)
L20(EA3): 12d8+8 (62)+4Stat (~33% less than 2H)
I suppose you can consider this balanced against the increasing AC differential due to magical shields existing.